a stage-sequential model of reading transitions: evidence ... · a stage-sequential model of...

Journal of Educational Psychology2005, Vol. 97, No.4, 551-563

Copyright 2005 by the American Psychological Association0022-0663/05/$12.00 DOl: 10.1037/0022-0663.97.4.551

A Stage-Sequential Model of Reading Transitions: Evidence From theEarly Childhood Longitudinal Study

David Kaplan and Sharon WalpoleUniversity of Delaware

This study uses latent transition analysis to examine reading development across the kindergarten and

1st-grade year. Data include poverty status and dichotomous measures of reading at 4 time points for a

large sample of children within the Early Childhood Longitudinal Study. In each of 4 waves of the study,5 latent classes were represented in different proportions: low alphabet knowledge, early phonological

processing, advanced phonological processing, early word reading, and early reading comprehension.Transition probabilities were calculated for the full sample and for children living above and below

poverty. The findings indicate that children living below poverty are less likely to experience successfulreading transitions than their above-poverty peers. However, children in the below-poverty group who

began kindergarten with at least early phonological processing experienced transition probabilities

similar to their above-poverty peers. Researchers should target and test preschool interventions for their

potential efficacy to mediate the effects of poverty on early reading.

Keywords: reading development, developmental transitions, poverty

This study addresses old and important questions. Are therediscrete stages in reading acquisition? If so, what is the likelihoodthat young children transition across these stages and into conven-tional reading by the end of first grade? We address this questionfirst for a large sample of children and then for an importantsubgroup: children living in poverty. As such, our findings may beof interest to those who study beginning reading from a theoreticalperspective, for those who design early reading interventions, forthose who establish educational policies designed to prevent read-ing failure, and for those who develop and apply advanced empir-ical methodologies to answer questions in the social sciences.

Stages in Reading Development

An underlying assumption tested in this article is that readersprogress through stages of development, and that those stages arequalitatively distinct, theoretically sound, and measurable. Stagetheories of reading development posit sequential and progressivemovement (Gillon, 2004). This assumption has a long history.Chall (1983) advanced what she called a "scheme" of six stages toorganize thinking about literacy development across the life span.Other researchers have focused their attention on stages within thecontext of reading acquisition (Ehri, 1987; Gibson, 1965;Gough &Hillinger, 1980; Juel, 1991; Mason, 1980).

EOO's (1995, 1999) recent phases of reading acquisition aremore fine grained than the general stages that Chall (1983) pro-posed. Each phase is characterized by the connection that a reader

David Kaplan and Sharon Walpole, School of Education, University ofDelaware.

Correspondence concerning this article should be addressed to David

Kaplan, School of Education, University of Delaware, Newark, DE 19716.E-mail: [email protected]

is making between the visual form of a word and its sound andmeaning stored in memory, and each connection is dependent onaccess to specific knowledge about print. In the prealphabeticphase, the connection is a default visual one; the reader does nothave the alphabet knowledge to link letters and sounds. In thepartial-alphabetic phase (because of some knowledge of letternames and sounds and some measure of phonological awareness),the reader can make a partial connection, usually only for theinitial and final letters. The full alphabetic phase includes connec-tions between all letters and the sounds they represent in words andfully amalgamated representations of sound, spelling, and meaningconnections in memory; it is dependent on automatic access toletter-sound information. Those connections facilitate transition to

the consolidated alphabetic phase, in which readers can make useof patterns larger than the individual letter sound (rimes, syllables,or morphemes); this phase is dependent on access to orthographicinformation. To achieve progress through Ehri's phases, then, anindividual would have to attain five specific early reading accom-plishments: alphabet knowledge, sensitivity to initial phonemes,sensitivity to final phonemes, full alphabetic decoding, and auto-matic word recognition. It is these five accomplishments that areinvestigated in this study.

The most salient criticisms of stage theories of reading acqui-sition target the strategies that individuals use to recognize andremember specific words rather than the underlying knowledgethat is required. Trieman and Bourassa (2000) moderate the use ofthe stage label to suggest that during reading acquisition, specificstrategies dominate (but may be used in concert with other strat-egies). For example, a child may recognize the word "cat" inrunning text by looking at the initial sound and using a picture cue.On that same page, the same child might recognize "can" auto-matically and effortlessly. That psychological flexibility wouldindicate cognitive functioning in more than one stage (partialalphabetic and consolidated alphabetic), consistent with Share's

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552 KAPLAN AND WALPOLE

(1995) self-teaching hypothesis; through a process of successfuldecoding of individual words, readers acquire item-specific knowl-edge rather than stage-based strategies. For this article, though, wefocus on.stages of acquisition of the foundational knowledge thatfacilitates recognition of unknown words without the benefit ofpicture cues rather than the specific cognitive strategies novicereaders use alone or in combination to read words in authenticrunning text. This focus is justified in that both stage and nonstagemodels of literacy acquisition depend on acquisition of specificknowledge about the alphabetic writing system (Rayner, Foorman,Perfetti, Pesetsky, & Seidenberg, 2001); recent work on the de-velopment of phonological sensitivity (Anthony, Lonigan,Driscoll, Phillips, & Burgess, 2(03) indicates that there is a cleardevelopmental sequence.

Indicators of Early Reading Success

To examine achievement over time, selection of powerful indi-cators is important both conceptually and empirically. Many re-searchers have pursued investigations of contextual influences onreading achievement and of intervention models to investigate theshort- and long-term relationships of specific indices of readingachievement amenable to instruction during the first years ofschool. These studies have produced convergent evidence thatattainment of specific subskills and more global language abilitiesearly in school are positively related to various forms of readingachievement later.

Unlike language acquisition, reading acquisition is not natu-ral-it depends to a large extent on access to appropriate oppor-tunities and instruction in and out of school. Therefore, under-standing the effects of context variables is essential. Variablesoutside the reader are related to various indices of reading achieve-ment or of response to interventions during the first years ofschool. Potentially powerful moderators of literacy growth haveincluded educational attainments of families or caregivers (e.g.,Burchifial, Peisner-Feinberg, Pianta, & Howes, 2002; Catts, Fey,Zhang, & Tomblin, 2001; Lyster, 2002), socioeconomic status(SES) of families (e.g., Alexander, Entwisle, & Olson, 2001;Dickinson & Snow, 1987), achievement measured at the schoollevel (e.g., Share, Jorm, MacLean, & Matthews, 1984), ethnicity(e.g., Alexander & Entwisle, 1988), and experience with literacyactivities at home (e.g., Bus, van Ijzendoorn, & Pellegrini, 1995).

All of the factors identified above are potentially related to thebroader issue of poverty, and there is ample evidence that povertyindices are inversely related to literacy achievement. The NationalAssessment of Educational Progress monitors that relationship forchildren beginning in Grade 4, and the results are grim. Forexample, in the year 2003, 55% of fourth-grade students whoqualified for federal lunch subsidies scored below the basic level inreading on the National Assessment of Educational Progress com-pared with 24% performance at this level for their more advan-taged peers (National Center for Education Statistics [NCES],2(01). This achievement gap is present from the start of school;kindergarten children's cognitive skills are related to their family'sincome (Gershoff, 2003). And unfortunately, persistent poverty,especially during the preschool years, is consistently associatedwith poor achievement in school later (Duncan & Brooks-Gunn,2000). Thus, increasing understanding of successful reading tran-

sitions is especially important to efforts to increase achievement ofpoor children.

There is a large literature that focuses on cognitive indicators ofearly reading success. Specifically, understanding letter names andsounds, development of full phonemic awareness, and the use ofthis combined knowledge and skill to read and spell unknownwords and to facilitate automatic sight word acquisition are doubt-less important aspects of reading acquisition. During the first 2years of school, these subskills include what Whitehurst and Loni-gan (2002) have termed "inside-out" skills: knowledge of letternames (e.g., Badian, 1995; Morris, Bloodgood, & Pemey, 2003;Scarborough, 1989;Share et al., 1984),knowledge of letter sounds(e.g., Scarborough, 1989),and phonological awareness (e.g., Shareet al., 1984; Stuart & Coltheart, 1988). Analyses that combinemeasurement of manyof the individual subskills above provide themost robust relationships with later literacy achievement (e.g.,Catts et al., 2001; Morris et aI., 2003; Schatschneider, Fletcher,Francis, Carlson, & Foorman, 2004). Analyses that measureachievement beyond the first-grade year contribute evidence that"outside-in" skills (Whitehurst & Lonigan, 2002), such as vocab-ulary knowledge and other oral language measures in kindergarten,are predictive of later achievement (Roth, Speece, & Cooper,2(02). How, when, and in what conditions these early accomplish-ments influence the development of even more complex readingskills are questions that have occasioned continuing theoretical,empirical, and practical investigation.

Transitions to Proficiency

Early indicators of literacy achievement are actually more im-portant when they are considered together for their long-termeffects on later reading achievement. Juel, Griffith, and Gough(1986) proposed and tested a "simple" model of literacy acquisi-tion in which phonemic awareness contributed to development ofcipher knowledge (decoding), which in turn contributed to bothword recognition and spelling. They examined these variables andothers across the first- and second-grade years using the method ofpath analysis; relationships in the data supported their model.Juel's (1988) longitudinal study of reading achievement for 54children from a low-SES neighborhood yielded a .88 probabilitythat a child who left kindergarten with weak phonemic awarenesswas a poor decoder at the end of first grade and would remain apoor decoder at the end of fourth grade. Juel's work turnedattention to early intervention, particularly during kindergarten andfirst grade.

Documenting the importance of proficiency in individual read-ing skills like phonemic awareness is not the same as understand-ing or predicting achievement for individual learners. In literacy,researchers are attempting to model a process that includes mul-tiple dimensions and is influenced by access to instruction. Duringreading acquisition, time is a factor that interacts with growth. Forexample, growth may not be linear and may be related to readers'ages and stages: Alexander and Entwisle (1988) found greatergrowth during the first-grade year than between the end of firstgrade and the end of second grade. Initial skills are also a factor toconsider. A study of reading development across the first 2 yearsof schooling in Finland (n = 196) found that although initialachievement levels were powerful predictors of reading at the endof Grade 1, growth in reading skills was not linear. In fact,

STAGE-SEQUENTIAL READING TRANSITIONS 553

individuals with higher levels of initial reading experienced morerapid growth in the 1st year of schooling, but individuals withlower initial literacy skills experienced more rapid growth duringthe 2nd year (Leppanen, Niemi, Aunola, & Nurmi, 2004). Thus,looking across time, we may be able to anticipate different growthtrajectories for children with different initial skills and to providethem with differentiated instructional opportunities to maximizetheir growth. In fact, observational work indicates that time, ex-plicitness, and teacher directedness interact to predict growth forchildren with different initial literacy skills at the start of firstgrade (Connor, Morrison, & Katch, 2004) and that different typesand amounts of word-level instruction may be needed to maximizeearly literacy growth for children with different levels of initialliteracy (Juel & Minden-Cupp, 2000; Xue & Meisels, 2004).

Modeling Stage-Sequential Processes:Latent Transition Analysis

Given the need to understand the development of salient literacyskills across the first years of school and the rich data available foruse in this study, selection of adequate methodology is crucial.Arguably, the most popular method for the analysis of change overtime is growth curve modeling (Raudenbush & Bryk, 2002; Willett& Sayer, 1994).Indeed, the power and popularity of growth curvemodeling and recent extensions to growth mixture modeling (Mu-then, 2002) are now well established in the array of quantitativemethodologies in the social and behavioral sciences. Applicationsof growth curve modeling and growth mixture modeling to theproblem of reading development can be found in several recentstudies (Francis, Shaywitz, Stuebing, Fletcher, & Shaywitz, 1996;Kaplan, 2003; Muthen, Khoo, Francis, & Kim Boscardin, 2002).

The importance of growth curve modeling notwithstanding, thismethod addresses only one conceptualization of change-namelythe rate of change over the time span of the data collection.Another conceptualization of change that arises in the social andbehavioral sciences especially relevant to early reading develop-ment concerns change in qualitative status over time. For example,concern may rest on changes in developmental states, such asPiaget's stages of cognitive development or Kohlberg's stages ofmoral development. In the context of this article, the problemcenters on stages of reading achievement during the transition toconventional reading in the first 2 years of school. Recent devel-opments and applications of latent transition analysis, a methodthat extends latent class analysis to problems of stage-sequentialdevelopment over time, allow its use to examine these readingtransitions.

This study applies latent transition analysis to a large longitu-dinal sample across the period of reading acquisition. Variablesinclude important indices of early reading achievement (alphabetknowledge, phonological awareness and letter sound knowledge,word reading, and early reading comprehension [ERC]) measuredrepeatedly and reliably at each of four time points. The followingresearch questions are considered:

1. Given data on important reading indicators for manyindividuals across the kindergarten and first-grade years,can we form latent classes?

2. Are these classes represented across the reading acquisi-tion window (kindergarten and first grade)?

3. Given membership in a given class, what is the proba-bility of movement into a successive class over time?

4. Is this probability of movement related to poverty status?

These questions are addressed by first performing separate la-tent class analyses for each wave of the study for the entire sampleand for each of two poverty levels. This is followed by a latenttransition analysis for the entire sample and by poverty level.Details regarding the latent transition analysis are discussed in theMethod section.

Method

Participants

This study uses data from the Early Childhood Longitudinal Study:

Kindergarten Class of 1998-1999 (ECLS-K; NCES, 2001). The ECLS-Kdatabase provides a unique opportunity for us to estimate the prospects of

successful reading achievement (which we define as the ability to com-

prehend text) by the end of first grade for children with different levels ofentering skill and different potential barriers to success. The ECLS-K dataavailable to address this question include longitudinal measures of literacy

achievement for a large and nationally representative sample;-a sample

unprecedented in previous investigations of early reading development.The ECLS-K is sponsored by the U.S. Department of Education and

NCES, and it is a component of the NCES longitudinal studies program.The ECLS-K has several major objectives. First, ECLS-K provides for the

study of achievement in the elementary school years. Second, ECLS-K

provides an assessment of the developmental status of children in theUnited States at the start of formal schooling and at various points through-

out the elementary school years. Third, ECLS-K allows for a cross-

sectional study of the nature and quality of kindergarten programs in the

United States. Finally, ECLS-K provides the necessary data to study the

relationship of family, preschool, and school experiences to developmental

status and growth during kindergarten and the elementary school years(NCES, 2001). It is this latter characteristic of ECLS-K that constitutes the

major focus of our investigation.The study design consists of a nationally representative sample of

approximately 22,000 children and their families attending more that 1,000

public and private schools.! Data collection took place during the fall of1998 and spring of 1999 (kindergarten), and fall of 1999 and spring of 2000(first grade). The survey continued during the spring of 2002 (third grade)

and spring of 2004 (fifth grade); however, public use data are, as of this

writing, only available for the first four waves of the survey. Data arecollected from children, their families, their teachers, and their schools. For

this study, only data on children and their families were relevant. Data onchildren were collected in untimed one-on-one assessments; data on fam-

ilies were collected through questionnaires.Data used for this article consist of the kindergarten base year (fall

1998/spring 1999) and fust-grade follow-up (fall 1999/spring 2000) panelsof ECLS-K. Only fust-time public school kindergarten students who were

! A multistage probability sampling design was used to produce a

nationally representative sample of the 1998-1999 U.S. kindergarten co-

hort. The primary sampling units were counties or groups of counties. Thesecond stage of the design consisted of schools sampled within the primarysampling units. The third stage of the design sampled students within

schools. Only Asians and Pacific Islanders were oversampled. Two stratawere created-one for the Asian and Pacific Islanders, and one for all other

children. Each child was sampled with equal probability and with a target

sample size of 24 children within each school. See NCES (2001) for moredetails.


promoted to and present at the end of first grade were chosen for this study.

The sampling design of ECLS-K included a 27% subsample of the totalsample at fall of the first grade to reduce the cost burden of following the

entire sample for four waves but to allow for the study of summer leamingloss (NCES, 2(01). Although this dramatically reduces the sample size, we

nevertheless include fall of fITSt grade in this study to allow four timepoints for estimation of the transition probabilities. The sample size for this

investigation is 3,575.

Measures and Instrument Design

The measures used in this study consist of a series of reading assess-

ments and a measure of poverty status. The measure of poverty is com-

puted by taking income information obtained from the parent survey andcomparing it against the 1998 Census poverty thresholds that vary accord-ing to household size. A dichotomous variable is provided that indicates

whether the child's household is below or above the poverty threshold.2

The reading assessments were conducted in an individual, untimed

format. The battery consisted of a first-stage routing test used to determine

which of three second-stage forms were administered (easy, middle, andhigh as indicated by difficulty level of the items). Using an item response

theory framework, we calculated reading scale scores for children on thebasis of their performance on the routing test and specific second-stage

form. The reading assessment contains items designed to measure basic

skills, those inside-out variables that Whitehurst and Lonigan (2002) have

identified as particularly salient in the first 2 years of school. Specifically,

the reading assessment yields scores for (a) letter recognition, (b) begin-ning sounds, (c) ending sounds, (d) sight words, and (e) words in context

(WIC). In the letter recognition subtest, four letters of the alphabet were

printed on a page and presented using a flipbook. The child named each of

the letters. In the beginning sounds subtest, six letters were presented on apage. The assessor said each of four target words out loud, and the child

pointed to the letter that made the same sound as at the beginning of eachstimulus word. The ending sounds subtest was conducted in the same way,

with the child pointing to the letter that made the same sound as occurredat the end of each stimulus word. The sight word subtest included four

words presented individually in isolation. The child was asked to read eachword. The WIC items included 4 sentence comprehension items. Theywere presented in a Cloze format. The child read each sentence and chose

among four response options for filling in the blank in the sentence.

In addition to reading scale scores, ECLS-K provides transformations of

these scores into probabilities of proficiency as well as dichotomous

proficiency scores, which we use in this study. To calculate dichotomous

proficiency scores, the ECLS-K instrument design formed clusters ofreading assessment items having similar content and difficulty. A child was

assumed to have passed a particular skill level if he or she answered at least

three of four items in the skill cluster correctly. A fail score was given ifthe child incorrectly answered or did not know at least two items within the

skill cluster. In the case of exactly two items correct, a pass/fail score was

given if the pattern of passes and fails for remaining proficiencies yielded

could suggest an unambiguous pass or fail. For example, a fail would beassigned if easier clusters had been failed, and no harder cluster had been

passed (NCES, 2(01) Therefore, for each student, there are five dichoto-

mous outcomes measured at four time points. The reading proficiencies

were assumed to follow a Guttman simplex model, in which mastery at aspecific skill level implies mastery at all previous skill levels. The model

we tested is a longitudinal Guttman simplex, examining how the parame-

ters of this model vary across poverty levels.

Analysis and Design

Briefly, latent transition analysis has its origins in the merging of

Markovstochasticprocessmodelsand latentclass models.Markovsto-chastic process models for the analysis of psychological variables were

initiated by Anderson (1954; as cited in Collins & Wugalter's, 1992,

study), and most applications at that time focused on single manifest

measures. However, as in the early work in factor analysis of intelligence

tests, researchers recognized that many important psychological variables

are latent-in the sense of not being directly observed but possibly mea-

sured by numerous manifest indicators.. The advantages to measuring

multiple latent variables via multiple indicators are the well-known bene-

fits with regard to reliability and validity. Therefore, it would be preferable

to model latent variables in the context of Markov processes and, in this

way, to provide an adequate representation of psychological constructs.

The appropriate measurement model for categorical latent variables is thelatent class measurement model.

Latent class models were introduced by Lazarsfeld and Henry (1968) for

the purposes of deriving latent attitude variables from responses to dichot-

omous survey items. In a traditional latent class analysis, it is assumed that

an individual belongs to one and only one latent class, and that given the

individual's latent class membership, the observed variables are indepen-

dent of one another-the so called local independence assumption (see

Clogg, 1995).3 The latent classes are, in essence, categorical factors arising

from the pattern of response frequencies to categorical items in which the

response frequencies playa role similar to that of the correlation matrix in

factor analysis (Collins, Hyatt, & Graham, 2(00). The analog of factor

loadings are parameters that estimate the probability of a particular re-

sponse to the manifest indicators given membership in the latent class.

Unlike continuous latent variables (factors), categorical latent variables

(latent classes) divide individuals into mutually independent groups.Of relevance to this article is the work of Wiggins (1973), who merged

the latent class measurement model with Markov stochastic process mod-

els. Contributions to the problem of estimation were made by van de Pol

and de Leeuw (1986) and van de Pol and Langeheine (1989). The difficultywith these models, as noted in Collins and Wugalter's (1992) study, was

that they focused on one single manifest indicator of the latent variable.

Such an indicator could be, they argued, unreasonably long and compli-

cated. The alternative would be to come up with simpler multiple manifest

categorical indicators of the categorical latent variable and combine them

with Markov stochastic process models.

The combination of multiple indicator latent class models and Markov

stochastic process models provided the foundation for latent transition

analysis of stage-sequential dynamic latent variables. According to Collins

and Wugalter (1992), stage-sequential dynamic latent variables are meta-

constructs comprised of other latent variables and the relations among them

(p. 134). At any given point in time, the array of latent class memberships

defines an individual's latent status. The problem then concerns estimation

of the transition probabilities from one latent status to another. In other

words, the concern is in estimating the transition probabilities of moving

across latent statuses over time and how these latent transition probabilities

differ as a function of relevant covariates. Latent transition analysis (Col-

lins & Wugalter, 1992) is used to estimate these transition probabilities and

fit the entire latent transition model to the observed pattern of response

frequencies over time. Throughout this article, data were analyzed with the

software program WinLTA (Collins, Lanza, Schafer, & Flaherty, 2002).4

WinL TA is a flexible software program that can be used to fit latent class

and latent transition models to data. A more detailed mathematical expo-

sition of latent transition analysis can be found in the Appendix.

2 In cases in which information on income was not obtained, a hot-deck

imputation procedure was used to assign income values (NCES, 2(01).

3 It may be interesting to note that latent class models are special cases

of latent Markov models in which latent class membership is not changingover time (Bijleveld & van der Kamp, 1998).

4 More detail regarding WinLTA canbe found at hnp:/lmethodology.psu.eduldownloads/winlta.htrnl


Table I

Descriptive Statistics for Poverty Level and Reading Assessments Across All Waves of ECLS-K

Results

The results of the latent transition analysis are presented first forthe whole sample and then for the two levels of poverty.

Full Sample Results

Descriptive statistics and split-half reliabilities for the fullsample analysis can be found in Table 1. Of note is that 81% ofthe sample is reported to be above poverty.5 Moreover, a carefulexamination of Table 1 reveals that there is considerable miss-ing data on the words in context measure for all time periodsexcept spring of first grade. It is important to note that in casesin which children did not answer enough items to unambigu-ously assign a pass or a fail, then ECLS-K protocol assigned apass or fail score if proficiency scores at other levels allowedfor an unambiguous assignment. For example, a pass could beinferred if harder clusters of items were passed, and no easierclusters of items were failed. The opposite logic was used toassign fail scores (NCES, 2001). This fact has bearing on ourstudy insofar as the most difficult cluster of items (comprehen-sion of WIC) had relatively few unambiguous scores of eitherpass or fail and was left blank in the ECLS-K database. In thatcase, and in other cases, we scored these items as fai\.6 We notethat the split-half reliabilities for the item clusters are relativelyhigh across the time points of this study.

The structure of the reading subtests as well as theoreticalconsiderations about the importance of alphabet knowledge,full phonemic awareness, decoding, and automatic word recog-nition led us to hypothesize that five latent classes wouldexplain the pattern of response frequencies to the five subtests.

Models specifying three and four latent classes were also spec-ified. The decision to reject the three and four class modelsrested on the pattern of response frequencies as well as theoverall fit of the model. As noted earlier, the response frequen-cies playa role similar to that of factor loadings in factoranalysis. Thus, the objective is to examine different structures(here 3 vs. 4 vs. 5 latent classes) with regard to ease ofinterpretation. The model with five latent classes showed betteroverall fit to the pattern of response frequencies and wassubstantively easier to explain.

Given the pattern of response probabilities (see Table 2), labelsfor the latent classes were generated. The low alphabet knowledge(LAK) class consisted of individuals with very low probability ofpassing any of the subtests. The early phonological processing(EPP) class consisted of individuals with moderate or high prob-ability of passing the letter recognition subtest, moderate proba-bility of passing the beginning sounds subtest (except in fall ofkindergarten), and low probability of passing the other three tests.The advanced phonological processing (APP) class consisted ofindividuals with high probability of passing the letter recognitionsubtest, moderate or high probability of passing the beginningsounds subtest, and, with the exception of the fall kindergarten

5 A weighted analysis shows that approximately 76% of the 1998 kin-dergarten cohort were above poverty, and 24% were below poverty.

6 The rationale for recoding blanks as fails rested on the computational

difficulties with the software in imputing missing data for such a large

model. We recognize that our results may be affected by this decision, butin smaller subsets of analyses that used missing data imputation, our results

were relatively robust when compared with the results of imputing fails.

n

Variable Valid Missing Proportion Variance Reliability'

Poverty level (I = above) 3,575 0 .81 .16FK: Letter recognition 3,516 59 .59 .37 .83FK: Beginning sounds 3,515 60 .26 .32 .76FK: Ending sounds 3,517 58 .12 .24 .72FK: Sight words 2,520 1,055 -.05 .13 .78FK: Words in context 368 3,207 -.52 .46 .60SK: Letter recognition 3,551 24 .86 .21 .79SK: Beginning sounds 3,551 24 .69 .30 .76SK: Ending sounds 3,551 24 .49 .34 .76SK: Sight words 3,359 216 .12 .20 .77SK: Words in context 762 2,813 .02 .44 .69Fl: Letter recognition 3,550 25 .90 .16 .77Fl: Beginning sounds 3,550 25 .79 .24 .73Fl: Ending sounds 3,549 26 .65 .30 .76Fl: Sight words 3,450 125 .24 .26 .80Fl: Words in context 1,191 2,384 .20 .37 .73SI: Letter recognition 3,552 23 .95 .09 .78SI: Beginning sounds 3,552 23 .92 .12 .70SI: Ending sounds 3,552 23 .88 .15 .68SI: Sight words 3,534 41 .80 .21 .78SI: Words in context 2,996 579 .51 .30 .73

Note. ECLS-K = Early Childhood Longitudinal Study: Kindergarten Class of 1998-1999; FK = fallkindergarten; SK = spring kindergarten; Fl = fall first grade; SI = spring first grade..Split half reliabilities of item-cluster scores based on proficiency levels.

Note. Response probabilities are for passed items. Response probabilities for failed items can be computedfrom 1 minus the probability (pass). LR = letter recognition; BS = beginning sounds; ES = ending sounds;SW = sight words; WIC = words in context; LAK = low alphabet knowledge; EPP = early phonemicawareness; APP = advanced phonemic awareness; EWR = early word reading; ERC = early readingcomprehension.a Class proportions within waves may not sum to 1.0 because of rounding error.

assessment, moderate or high probability of passing the endingsounds subtest. The early word reading (EWR) class consisted ofindividuals with high probability of passing letter recognition,beginning sounds, and ending sounds, and low or moderate prob-ability of passing the sight word subtest (except in spring ofkindergarten). Finally, the ERC class consisted of individuals withhigh probability of passing letter recognition, beginning sounds,ending sounds, and sight words, and either moderate or highprobability of passing the WIC subtest.

Table 2 presents the response probabilities measuring thedynamic latent variables conditional on latent status member-ship. The interpretation of this table is similar to the interpre-tation of a factor loading matrix. Specifically, we examine theresponse probabilities for five subtests given the latent class.So, for example, in the fall of kindergarten, given membershipin the LAK class, the probability of passing any of the subtestsis very low. In contrast, given membership in the ERC class, theresponse probabilities on all but the WIC subtest are very high.We conclude that the pattern of response probabilities acrossthe subtests and across time corroborate our theoretically pre-dicted latent classes.

The last column ofT able 2 presents the latent class membershipproportions across the four ECLS-K waves for the full sample. We

see that in fall of kindergarten, approximately 18% of the cases fallinto the LAK class, whereas only approximately 3% of the casesfall into the ERC class. This breakdown of proportions can becompared with the results for spring of first grade; by that time,only 3% of the sample are in the LAK class, whereas approxi-mately 40% of the sample is in the ERC class.

The latent class membership proportions displayed in Table 2indicate that there is some movement to more advanced classes

over time. However, Table 2 does not provide the transitionprobabilities for individuals given their membership in a spe-cific latent class. The transition probabilities for the full samplecan be found in Table 3. An inspection of Table 3 reveals thatfor fall of kindergarten, children in the LAK class have a .53probability of staying in that class in the spring of kindergartenand a .46 probability of moving to the next latent class. The"stayer" probabilities can be found in the diagonal elements ofthe table, whereas the "mover" probabilities can be found in theoff-diagonal elements. To take another example, children in theAPP class in the fall of first grade have a .11 probability ofstaying in that class but a .64 probability of moving to the EWR

class and a .25 probability of moving to ERC in the spring offirst grade. The five-class latent transition model for the full


Table 2

Response Probabilities to Items Measuring the Dynamic Latent Variable Conditional on LatentReading Status and Time for Full Sample

Subtests

Wave LR BS ES SW WIC Class proportions.

Fall kindergartenLAK .00 .00 .00 .00 .00 .18EPP .60 .03 .02 .00 .00 .39APP .96 .59 .18 .00 .00 .28EWR .99 .99 .90 .01 .00 .11ERC 1.00 .96 .91 .97 .38 .03

Spring kindergartenLAK .03 .05 .00 .00 .00 .10EPP .97 .35 .07 .00 .00 .20APP .99 .91 .58 .01 .00 .38EWR 1.00 .97 .91 .23 .01 .23ERC 1.00 .98 .97 .98 .55 .09

Fall first gradeLAK .12 .05 .01 .00 .00 .07EPP .96 .57 .14 .01 .00 .19APP .99 .93 .80 .04 .00 .41EWR .99 .99 .96 .63 .03 .23ERC 1.00 .99 .98 .99 .91 .10

Spring first gradeLAK .04 .00 .00 .00 .00 .03EPP .95 .69 .19 .11 .00 .05APP .96 .93 .93 .00 .03 .12EWR 1.00 .97 .95 1.00 .11 .40ERC 1.00 .99 .98 1.00 .98 .40

Note. Blank subdiagonal elements indicate a longitudinal Guttman process. LAK = low alphabet knowledge;EPP = early phonemic awareness; APP = advanced phonemic awareness; EWR = early word reading; ERC =early reading comprehension."Wave (j). b Rows in the transition matrix may not sum to 1.0 because of rounding error. C Fixed to 1.0 bydesign.

sample was found to fit the data (LJul/ == 1,048,440, P > .05).7

2167.073, df

Poverty Level Differences

In this section, we examine differences in the achievement ofchildren living above and below the poverty threshold on aspectsof the latent transition analysis-specifically response probabili-ties, latent class membership proportions, and transition probabil-ities. Our comparative results are descriptive in nature in that noattempt was made to assess whether differences between povertygroups were statistically significant.

Table 4 presents the response probabilities and latent classmembership proportions for each poverty status. An inspection ofTable 4 reveals that the pattern of response probabilities is roughlythe same for each latent class for children living above and belowthe poverty threshold. Although there are differences, they arerelatively minor and lead us to the conclusion that the naming ofthe latent status variables applies to data for both groups.

The static latent class membership proportions for each povertylevel can be seen in the 7th and 13th columns of Table 4. A closeinspection of this table indicates that for any given wave ofECLS-K, children living below poverty are more represented inthe lower skill level classes than children living above poverty. Forexample, in the spring of kindergarten, approximately 7% of thechildren living above poverty are in the LAK class compared with

approximately 24% of children living below poverty. By contrast,approximately 24% of the children living above poverty are mem-bers of the EWR class, compared with 13% of the children livingbelow poverty. These patterns are roughly the same across thewaves of ECLS-K.

As noted in the analysis for the full sample, Table 4 does notprovide the transition probabilities associated with moving acrossstatuses over time. The results in Table 5 provide the transitionprobabilities for each poverty status. An inspection of Table 5reveals interesting and suggestive patterns. First, note that childrenliving above poverty tend to transition into the next status atsomewhat higher rates than children living below poverty. Forexample, in the spring of kindergarten, children living abovepoverty and in the LAK class have a .60 probability of staying inthat class and a .27 probability of moving to the next latent classby the fall of first grade. By comparison, children below poverty

7 The degrees of freedom for a latent transition model are obtained from

subtracting the number of parameters to be estimated from the total numberof possible response patterns. In the case of this analysis, there are 5(subtests) x 4 (waves) = 20 elements. The total number of response

patterns is 220 = 1,048,576 possible response patterns. There are 136 freeparameters to be estimated. Hence, the degrees of freedom = 1,048,440

(see the Appendix for more details).


Table 3

Transition Probabilities From Fall Kindergarten to Spring First Grade for Full Sample:First-Order Effects Only

Wave (i) LAK EPP APP EWR ERC

Spring kindergarten"

Fall KindergartenLAK .53 .46 .01 .00 .OlbEPP .30 .66 .04 .00APP .41 .55 .04EWR .60 .40ERC 1.()(f

Fall first grade"

Spring kindergartenLAK .70 .23 .05 .03 .00EPP .83 .16 .01 .00APP .99 .01 .00EWR .93 .07ERC 1.00

Spring first grade"

Fall first gradeLAK .40 .33 .17 .10 .00EPP .14 .32 .54 .00APP .11 .64 .25EWR .14 .86ERC 1.00


Table 4

Response Probabilities to Items Measuring the Dynamic Latent Variable Conditional on Latent Reading Status and Time

have a .81 probability of staying in the LAK class and only a .17probability of moving to the EPP class by the fall of first grade.

At the beginning of kindergarten, the EPP class experienceshigh transition probabilities for children above and below poverty.That attainment of both alphabet knowledge and the ability tosegment initial sounds during the preschool years may be anespecially powerful predictor of later reading success. Similartransitions are evident during the first-grade year for the EPPcategory. However, children from poverty are less likely to movefrom EPP to EWR than those living above poverty, and arguablyfew from either poverty group are able to progress from EPP toERe.

Other suggestive patterns emerge from an inspection of Table 5.Specifically,we observe that in the early waves of ECLS-K, move-ment into the later skillclassesis not appreciablydifferentforchildrenliving above or below poverty.For example, in the fall of kindergar-ten, children living above poverty and in the EWR class have a .58probabilityof stayingin that class and a .42 probabilityof moving tothe highest level, the ERC class. Comparable probabilitiescan befound for children living below poverty. This finding suggests thatvery high skill levels at entry into a grade can mitigatethe effects ofpoverty.Regardless,we find thatpovertydoes constrainthe transitionof children to higher levelsof reading,particularlyfor the early set ofskills. It should be noted that the model for the abovepovertysampleand below poverty sample show excellent fit to the data [L~ove

= 1836.735,df = 1,048,440,P > .05;L~elow= 728.358,df= 1,048,440,p > .05, respectively].

Discussion

This study investigated reading transitions during the first 2years of school for a large and nationally representative sample ofchildren. Reading achievement was defined in the data set used forthis study to include letter recognition, knowledge of initial soundsin words, knowledge of final sounds in words, word reading inisolation, and sentence-level comprehension. Given the literatureon reading development, we assumed these accomplishments to besuccessively more complex; our data supported that assumption.The methodology used in this study, latent transition analysis,allowed us to investigate whether there were similar latent classesfor groups of individuals in the study at each of four time pointsand to estimate the probability that individual members in a latentclass would progress to membership in a more advanced latentclass between start and end of kindergarten, between end ofkindergarten and start of first grade, and between start of firstgrade and end of first grade. We found five latent classes to existin different proportions at different times: LAK, EPP, APP, EWR,and ERe. Given these five classes and the analysis available to us,we were able to calculate transition probabilities for the fullsample and separately for children living in poverty and for thosenot living in poverty.

Contributions of This Study

Givenmeasuresofalphabetknowledge,phonemicawareness,decoding,and sentence-level reading comprehension during kindergarten and first

Above poverty Below povertyClass Class

Wave LR BS ES SW WIC proportions LR BS ES SW WIC proportions

Fall kindergartenLAK .02 .02 .01 .00 .00 .24 .01 .01 .00 .00 .00 .38"EPP .87 .01 .00 .00 .00 .29 .44 .01 .02 .00 .00 .41APP .94 .66 .23 .00 .00 .31 .94 .34 .00 .00 .00 .13EWR .99 .99 .90 .00 .00 .12 .98 .87 .63 .05 .00 .09ERC 1.00 .96 .92 .97 .36 .03 1.00 1.00 1.00 1.00 1.00 .00

Spring kindergartenLAK .10 .11 .01 .00 .00 .07 .00 .02 .00 .00 .00 .24EPP .99 .44 .000 .00 .00 .19 .96 .15 .00 .00 .00 .23APP .99 .92 .63 .01 .00 .41 .99 .78 .00 .00 .00 .34EWR 1.00 .97 .91 .30 .01 .24 1.00 .98 .91 .08 .00 .13ERC 1.00 .98 .97 .98 .56 .10 1.00 .95 .94 .96 .20 .06

Fall first gradeLAK .27 .05 .01 .00 .00 .04 .04 .06 .01 .00 .00 .19EPP .98 .65 .21 .01 .00 .18 .96 .43 .06 .00 .00 .25APP .99 .94 .85 .05 .00 .42 .98 .88 .60 .03 .00 .36EWR .99 .98 .95 .69 .04 .23 1.00 .95 1.00 .30 .00 .14ERC 1.00 .99 .98 .99 .92 .20 1.00 .96 1.00 1.00 .51 .07

Spring first gradeLAK .25 .00 .00 .00 .00 .02 .06 .00 .00 .00 .00 .09EPP 1.00 .91 .76 .29 .02 .11 .97 .77 .41 .09 .00 .19APP 1.00 .37 .44 .00 .00 .01 1.00 .96 .95 .69 .02 .42EWR 1.00 .97 .96 .90 .13 .42 .96 .89 .96 .87 .00 .08ERC 1.00 .99 .98 1.00 .99 .45 1.00 1.00 .99 1.00 .92 .22

Note. Response probabilities are for passed items. Response probabilities for failed items can be computed from 1 - probability (pass). LR = letterrecognition; BS = beginning sounds; ES = ending sounds; SW = sight words; WIC = words in context; LAK = low alphabet knowledge; EPP = earlyphonemic awareness; APP = advanced phonemic awareness; EWR = early word reading; ERC = early reading comprehension."Class membership proportions within waves may not sum to 1.0 because of rounding error.

grade, this study provides evidence of a sequential order of knowledge

acquisition. Namely, literacy knowledge advances from letter recognitionto sensitivity to beginning sounds and their graphemes, to sensitivity to

ending sounds and their graphemes, to word reading, and to sentence-level

comprehension during the fIrst 2 years of school. The testing protocolallowed for different patterns, namely that individuals could be successful

in more diffIcult tasks without success on easier ones, but inspection of

Table 2 indicates that there was very little variation in performance. Given

four different time points, and fIve different measures, our analysis pro-duced fIve stable latent classes. Within each class, the relationships among

the variables of interest were fairly stable; high probability of passing the

beginning sounds task was achieved only after mastery of the alphabet

knowledge task; high probability of passing the sight word task wasachieved only after mastery of ending sounds; high probability of passing

the WIC task was achieved only after mastery of all other tasks and only

during fust grade. Only in the ERC class did mastery of more complextasks not appear totally dependent on mastery of less complex ones for a

small portion of the sample; however, in this class, mastery scores were

nearly perfect for all indicators.This study provides estimates of the proportions of children with par-

ticular reading skill profIles at each of four important transition points:

beginning and end of kindergarten, and beginning and end of fIrst grade. Atthe beginning of kindergarten, relatively few individuals had suffIcient

alphabet knowledge and phonological awareness to facilitate word reading;

at the end of kindergarten and the beginning of fust grade, approximately70% of these same individuals had attained at least APP; by the end of fIrst

grade, 80% of the these individuals had attained at least EWR. In an era of

high-stakes, assessment -driven school accountability, these are promisingtrends. However, a comparison of achievement by poverty level gives a

different picture. At the start of kindergarten, more children living in

low-SES households began reading instruction with LAK compared with

their peers living above poverty; by the spring of kindergarten, 75% ofchildren living above poverty had attained at least APP, whereas only 53%

of their peers living below poverty had. In fall of fust grade, 43% of the

cohort living above poverty were at EWR or ERC compared with 21% ofthe cohort living below poverty. By the end of fIrst grade, 87% of the

cohort living above poverty were at least early word readers, whereas only

30% of their peers with fewer economic resources had achieved at thatsame level.

The transition probabilities for children above and below poverty are

also compelling (see Table 5). Between fall and spring of kindergarten,children who enter kindergarten with at least EPP were relatively likely to

progress, regardless of their poverty status. Unfortunately, the large num-ber of children living below poverty and in the LAK class tended to make

no movement even with a year's instruction. During the summer months,

in the absence of instruction, the outlook for those children was also grim;60% of the children in the low-alphabet-knowledge class who were above

poverty maintained their latent class membership (but 40% moved),

whereas 81 % of the children living below poverty maintained their latentclass membership (with only 19% moving). In the fall of fIrst grade,

children above poverty with at least APP were almost certain to progressbeyond that level. However, children below poverty, beginning at that

same status (APP) were unlikely to progress. In fact, the probability of .86

for the below-poverty cohort not to progress beyond APP by the end of fustgrade harkens directly to Juel's (1988) finding that poor readers, especially

those who leave kindergarten with weak phonological skills, tend not toexperience success later. It appears that children living in poverty who start

fIrst grade with APP but not EWR are much less likely to progress during


Table 5

Transition Probabilities From Fall Kindergarten to Spring First Grade: First-Order Effects Only

Above poverty Below poverty

Wave (i) LAK EPP APP EWR ERC LAK EPP APP EWR ERC

Spring kindergarten"

Fall KindergartenLAK .30 Al .28 .00 .00b .63 .25 .10 .02 .00EPP .29 .62 .09 .00 .35 .63 .00 .02APP .50 .46 .04 .35 .64 .01EWR .58 .42 .46 .54ERC 1.00c 1.00

Fall fIrst grade"

Spring kindergartenLAK .60 .27 .11 .02 .00 .81 .17 .00 .02 .00EPP .87 .13 .00 .00 .87 .06 .06 .00APP .96 .04 .00 1.00 .00 .00EWR .91 .09 .96 .04ERC 1.00 1.00

Spring fIrst grade"

Fall fIrst gradeLAK 042 .56 .00 .00 .02 .45 Al .14 .00 .00EPP .46 .01 .54 .00 047 .35 .15 .03APP .01 .70 .29 .86 .00 .14EWR .11 .89 .30 .70ERC 1.00 1.00

Note. Blank subdiagonal elements indicate a longitudinal Guttman process. LAK = low alphabet knowledge; EPP = early phonemic awareness; APP =advanced phonemic awareness; EWR = early word reading; ERC = early reading comprehension.

a Wave (j). b Rows in the transition matrix may not sum to 1.0 because of rounding error. C Fixed to 1.0 by design.


first grade than their peers living above poverty. This relative disadvantage

seems to apply only to children living in poor households; Phillips, Norris,

Osmond, and Maynard (2002) found that first graders with below-averagereading achievement were equally likely to be either below average or

average achievers in sixth grade; their initial low-achievement status wasnot necessarily maintained.

The findings in this study that poverty moderates transition probabilitiesearly in schooling can be used in combination with the large literature on

interventions that target early reading achievement (e.g., Bus & van Ijzen-

doorn, 1999; Morris, Tyner, & Perney, 2000; Rashotte, MacPhee, &

Torgesen, 2001; Torgesen, 2000; Torgesen, Morgan, & Davis, 1992;Vellutino et al., 1996; Vellutino & Scanlon, 2(02) and the policy-oriented

focus on improving instruction during the primary school years (No ChildLeft Behind Act of 2001). Specifically, schools implementing federally

funded reform of instruction during kindergarten and first grade will be

improving opportunities for reading acquisition by using instructional

strategies and curriculum materials informed by the results of experimentalstudies of reading instruction. They will also be tracking individual student

progress over time. Important questions could be answered within these

cohorts. Given access to high-quality curriculum during kindergarten andfirst grade, what are the transition probabilities for children? Are they

different for children living in poverty? To what extent? Latent transition

analysis applied to assessment data for these new samples would yieldimportant new information about literacy transitions for children receiving

relatively similar instructional opportunities.Given that these reform models typically rely on prevention-based

classroom instruction and costly one-on-one tutoring or smaIl-group inter-

ventions, accurate identification of only those children whose success

depends on this attention early in their schooling is essential from aresource-allocation stance. Our study suggests that timing matters, espe-

cially for children living in poverty. Between fall and spring of kindergar-

ten and between spring of kindergarten and fall of first grade, children with

LAK are unlikely to progress to more advanced understandings. That time,then, is an especially important one for testing the efficacy of interventions

and their effect on these transitions. Similarly, all children are unlikely to

make progress in their basic reading skills during the summer monthsbetween kindergarten and first grade; given this finding and the work of

others on the importance of summer (e.g., Alexander et aI., 2(01), this isanother time when the impact of intervention on children's literacy tran-

sitions might be explored. Finally, for those children who enter first gradewith advanced phonemic awareness, children living in poverty are much

less likely than their peers with more economic advantages to move to

EWR or ERC; interventions which target the achievement of these children

during the first -grade year may have profound effects on their literacytransitions.

Other avenues for research include examinations of the impact of pre-

school on future literacy transitions, particularly for children living in

poverty. In our study, we provide estimates of the relative size of mem-

bership in each of five latent classes for each of four time points (see Table4). At the very outset of formal schooling, 13% of the individuals living inpoverty in our cohort had already achieved APP, and these children had a

high probability of transition to EWR during kindergarten. Explorations of

the experiences of those children who come to school with advanced

knowledge could inform interventions for children living in poverty duringthe preschool years.

Limitations

We acknowledge several limitations to this work, both substan-tive and methodological. In the substantive arena, we have notaddressed all possible variables that might influence the charac-teristics of latent classes or the transition probabilities. Specifi-

cally, measures of naming speed have beenreliably associatedwith literacy achievement, both for struggling beginning readers

and for poor children (e.g., Hecht, Burgess, Torgesen, Wagner, &Rashotte, 2000; Schatschneider et al., 2004; Torgesen & Davis,1992); those data were not available to us. Additionally, weinvestigate reading development in the first years of school with-out addressing the instructional context. Although the data set islarge and includes individuals from many schools, we do notaccount for the different instructional opportunities presented tothese children in our analyses. In fact, a recent study that used theECLS data set did find that teacher reports about the content oftheir instruction during kindergarten were related to differentialachievement outcomes, particularly when initial skills were in-cluded as variables (Xue & Meisels, 2004).

There are three methodological limitations that we would like toacknowledge. First, we have opted to code missing data, particu-larly on the word recognition in context task, as failure. We madethis decision to count these as failures given our assumption thatthe accomplishments measured in the ECLS-K data set are suc-cessive, and, therefore, an ambiguous score on the most complexitems was the same as a failure. Second, this work is descriptive.No statistical significance tests were used to compare differencesamong the latent transition probabilities. Given the number ofpossible significance tests that could have been performed, it wasfelt that the essential points of the this article would have been lostin trying to explain the myriad of significance tests. Instead, wesimply reported the tests of overall model fit to the responsefrequencies. Third, we have assumed that there are no othercovariates (observed or unobserved) that can explain differences intransition probabilities across poverty levels. A flexible feature oflatent transition analysis is the incorporation of latent class covari-ates in the model. For example, suppose in addition to the observedpoverty indicator, we added indicators of different behavior prob-lems. In line with Equation A2 in the Appendix, these indicatorscan be used to form latent behavior problem classes. Those classescan be incorporated into the general model as shown in EquationAI. Indeed, our poverty status variable could have been incorpo-rated in a single analysis, but difficulty with the convergence of thesoftware program for such a large model forced us to treat povertygroups separately. This study, therefore, serves a pedagogicalfunction in demonstrating the use of latent transition analysis. Weencourage additional studies that draw on the full functionality ofthe methodology.

References

Alexander, K. L., & Entwisle, D. R. (1988). Achievement in the first 2

years of school: Patterns and processes. Monographs of the Society for

Research in Child Development, 53, pp. 1-157.Alexander, K. L., Entwisle, D. R., & Olson, L. S. (2001). Schools,

achievement, and inequality: A seasonal perspective. Educational Eval-uation and Policy Analysis, 23. 171-191.

Anthony, J. L., Lonigan, C. J., Driscoll, K., Phillips, B. M., & Burgess,

S. R. (2003). Phonological sensitivity: A quasi-parallel progression orword structure units and cognitive operations. Reading Research Quar-terly, 38,470-487.

Badian, N. (1995). Predicting reading ability over the long term: The

changing roles of letter naming, phonological awareness, and ortho-

graphic processing. Annals of Dyslexia, 45, 79-96.Bijleveld, C. & van der Kamp, L. (1988). Longitudinal data analysis:

Designs,models. and methods. Newbury Park, CA: Sage.Burchinal, M. R., Peisner-Feinberg, E., Pianta, R., & Howes, C. (2002).

STAGE-SEQUENTIAL READING TRANSITIONS

Development of academic skills from preschool through second grade:

Family and classroom predictors of developmental trajectories. Journal

of Sclwol Psychology, 40, 415-436.

Bus, A. G., & van Ijzendoorn, M. H. (1999). Phonological awareness and

early reading: A meta-analysis of experimental training studies. Journal

of Educational Psychology, 91, 403-414.

Bus, A. G., van Ijzendoorn, M. H., & Pellegrini, A. D. (1995). Joint book

reading makes for success in leaming to read: A meta-analysis on

intergenerational transmission of literacy. Review of Educational Re-search. 65. 1-21.

Catts, H. W., Fey, M. E., Zhang, X., & Tomblin, J. B. (2001). Estimating

the risk of future reading difficulties in kindergarten children: A

research-based model and its clinical implementation. Language.

Speech. and Hearing Services in Schools. 32. 38-50.

Chall, J. S. (1983). Stages of reading developrrumt. New York: McGraw-Hill.

Clogg, C. C. (1995). Latent class models. In G. Arminger, C C. Clogg, &

M. E. Sobel (Eds.), Handbook of statistical modeling in the social and

behavioral sciences (pp. 81-11 0). San Francisco: Jossey-Bass.

Collins, L M. (2002). Latent transition analysis for Windows (Version

3.0). State College, PA: Pennsylvania State University, University Park

Campus, Methodology Center.Collins, L M., Hyatt, S. L, & Graham, J. W. (2000). Latent transition

analysis as a way of testing models of stage-sequential change in

longitudinal data. In T. D. Little, K. U. Schnabel, & J. Baumert

(Eds.), Modeling longitudinal and multilevel data: Practical issues,

applied approaches, and specific examples (pp. 147-161). Mahwah, NJ:Erlbaum.

Collins, L M., Lanza, S. T., Schafer, J. L, & Raherty, B. P. (2002).

WinLTA user's guide. State College, PA: Pennsylvania State University,

University Park Campus, Methodology Center.

Collins, L M., & Wugalter, S. E. (1992). Latent class models for stage-

sequential dynamic latent variables. Multivariate Behavioral Research.27, 131-157.

Connor, eM., Morrison, F. J., & Katch, L E. (2004). Beyond the reading

wars: Exploring the effect of child-instruction interactions on growth in

early reading. Scientific Studies of Reading. 8. 305-336.

Dempster, A. P., Laird, N. M., & Rubin, D. B. (1977). Maximum likeli-

hood from incomplete data via the EM algorithm (with discussion).

Journal of the Royal Statistical Society, Series B, 39. 1-38.Dickinson, D. K., & Snow, C E. (1987). Interrelationships among pre-

reading and oral language skills in kindergartners from two social

classes. Early Childhood Research Quarterly. 2, 1-25.

Duncan, G. J., & Brooks-Gunn, J. (2000). Family poverty, welfare refonn,

and child development. Child Development. 71, 188-196.

Ehri, L (1987). Learning to read and spell words. Journal of ReadingBehavior. 19. 1-31.

Ehri, L (1995). Phases of development in leaming to read words by sight.

Journal of Research in Reading. 18. 116-125.Ehri, L (1999). Phases of development in learning to read words. In J.

Oakhill & R. Beard (Eds.), Reading development and the teaching of

reading: A psyclwlogical perspective (pp. 79-108). Oxford, England:Blackwell.

Francis, D. J., Shaywitz, S. E., Stuebing, K. K., Retcher, J. M., &

Shaywitz, B. A. (1996). Developmental lag versus deficit models of

reading disability: A longitudinal individual growth curves analysis.

Journal of Educational Psychology. I, 3-17.

Gershoff, E. (2003). Low income and the development of America's kin-

dergarteners (Research Brief No.4). New York: National Center forChildren in Poverty.

Gibson, E. J. (1965, May 21). Learning to read. Science, 148. 1066-1072.

Gillon, G. T. (2004). Phonological awareness: From research to practice.New York: Guilford Press.

561

Gough, P. B., & Rillinger, M. L (1980). Learning to read: An unnaturalact. Bulletin of the Orton Society, 30, 179-196.

Hecht, S. A., Burgess, S. R., Torgesen, J. K., Wagner, R. K., & Rashotte,

C A. (2000). Explaining social class differences in growth of reading

skills from beginning kindergarten through fourth-grade: The role of

phonological awareness, rate of access, and print knowledge. Readingand Writing: An Interdisciplinary Journal, 12. 99-127.

Juel, C (1988). Leaming to read and write: A longitudinal study of

fifty-four children from first through fourth grades. Journal of Educa-tional Psychology, 80. 437-447.

Juel, C. (1991). Beginning reading. In R. Barr, M. L Kamil, P. Mosenthal,

& P. D. Pearson (Eds.), Handbook of reading research (Vol. 2, pp.759-788). Mahwah, NJ: Erlbaum.

Juel, C, Griffith, P., & Gough, P. (1986). Acquisition of literacy: A

longitudinal study of children in first and second grade. Journal ofEducational Psychology. 78, 243-255.

Juel, C, & Minden-Cupp, C (2000). Learning to read words: Linguistic

units and instructional strategies. Reading Research Quarterly, 35, 458-492.

Kaplan, D. (2003). Methodological advances in the analysis of individual

growth with relevance to education policy. Peabody Journal of Educa-tion. 77. 189-215.

Lanza, S. T., & Collins, L M. (2002, March). Pubertal timing and the onset

of substance use in females during early adolescence. Prevention Sci-ence. 3, 69-82.

Lazarsfeld, P. F., & Henry, N. W. (1968). Latent structure analysis.

Boston: Houghton Mifflin.

Leppanen, U., Niemi, P., Aunola, K., & Nurmi, J. (2004). Development of

reading skills among preschool and primary school pupils. ReadingResearch Quarterly, 39. 72-93.

Little, R. J. A., & Rubin, D. B. (2002). Statistical analysis with missingdata (2nd ed.). New York: Wiley.

Lyster, S. A. H. (2002). The effects of morphological versus phonological

awareness training in kindergarten on reading development. Reading

and Writing: An Interdisciplinary Journal. 15. 261-294.

Mason, J. M. (1980). When do children begin to read?: An exploration of

four-year-old children's letter- and word-reading competencies. ReadingResearch Quarterly, 15. 203-227.

Morris, D., Bloodgood, J., & Perney, J. (2003). Kindergarten predictors of

first- and second-grade reading achievement. Elementary School Jour-nal, 104. 93-109.

Morris, D., Tyner, B., & Pemey, J. (2000). Early steps: Replicating the

effects of a first-grade reading intervention program. Journal of Educa-

tional Psychology. 92. 681-693.

Muthen, B. O. (2002). Beyond SEM: General latent variable modeling.Behaviormetrika, 29, 81-117.

Muthen, B., Khoo, S. T., Francis, D., & Kim Boscardin, C (2002).

Analysis of reading skills development from kindergarten through first

grade: An application of growth mixture modeling to sequential pro-

cesses. In S. R. Reise & N. Duan (Eds.), Multilevel modeling: Metlwd-

ological advances. issues, and applications (pp. 71-89). Mahwah, NJ:Erlbaum.

National Center for Education Statistics. (2001). Early Childhood Longi-

tudinal Study: Kindergarten Class of 1998-1999: Base year public-usedata files user's manual (No. NCES 2001-029). Washington, DC: U.S.

Government Printing Office.No Child Left Behind Act of 2001, PL 107-110, 115 Stat. 1425,20 U.S.C.

§§ 6301 et seq.

Phillips, L M., Norris, S. P., Osmond, W. C, & Maynard, A. M. (2002).

Relative reading achievement: A longitudinal study of 187 children from

first through sixth grades. Journal of Educational Psychology, 94, 3-13.Rashotte, C. A., MacPhee, K., & Torgesen, 1. K. (2001). The effectiveness

of a group reading instruction program with poor readers in multiple

grades. Learning Disability Quarterly, 24, 119-134.


Raudenbush, S. W., & Bryk, A. S. (2002). Hierarchical linear models:

Applications and data analysis methods (2nd ed.). Thousands Oaks, CA:

Sage.

Rayner, K., Foorrnan, B. R., Perfetti, C. A., Pesetsky, D., & Seidenberg,

M. S. (-200l). How psychological science infonns the teaching of read-

ing. Psychological Science in the Public Interest, 2, 31-74.Roth, F. P., Speece, D. L., & Cooper, D. H. (2002). A longitudinal analysis

of the connection between oral language and early reading. Journal ofEducational Research, 95, 259-272.

ScarlJorough, H. S. (1989). Prediction of reading disability from familiar and

individual differences. Journal of Educational Psychology, 81, 101-108.Schatschneider, C., Aetcher, J. M., Francis, D. J., Carlson, C. D., &

Foorrnan, B. R. (2004). Kindergarten prediction of reading skills: Alongitudinal comparative analysis. Journal of Educational Psychology,96, 265-282.

Share, D. (1995). Phonological recoding and self-teaching: Sine qua non of

reading acquisition. Cognition, 55, 151-218.Share, D., Jorm, A., MacLean, R., & Matthews, R. (1984). Sources of

individual differences in reading acquisition. Journal of EducationalPsychology, 76, 1309-1324.

Stuart, M., & Coltheart, M. (1988). Does reading develop in a sequence of

stages? Cognition, 30, 139-181.Torgesen, J. K. (2000). Individual differences in response to early inter-

ventions in reading: The lingering problem of treatment resisters. Learn-ing Disabilities Research and Practice, 15, 55-64.

Torgesen,1. K., Morgan, S., & Davis, C. (1992). The effects of two types

of phonological awareness training on word learning in kindergartenchildren. Journal of Educational Psychology, 84, 364-370.

Trieman, R., & Bourassa, D. C. (2000). The development of spelling skill.

Topics in Language Disorders, 20, 1-18.

This appendix provides a brief overview of the mathematical model

underlying latent transition analysis, following closely the discussion given

in the fgllowing studies: Collins & Wugalter (1992) and Lanza & Collins(2002). eWe concentrate on the models relevant to this article, recognizing

that more general models can be estimated. For simplicity of notation,

assume that there are only two time periods being measured. Generaliza-tion to all four time periods will be obvious.

To begin, denote the fIrst wave of measurement as time t and the secondwave of measurement as time t + 1. Assume that there are three manifest

indicators (e.g., reading subtests). The first indicator has i', i"= 1,2,. ..1 response categories, the second indicator has j',f'= 1,2,...1, and the third manifest indicator has k' ,f(' = 1,2,.. .K, where

i', j', and k' refer to the responses obtained at time t, and i", f', and f(' are

the responses obtained at time t + I. In our case, there are two response

categories, but it is clear from the notation that more than two categoriescan be accommodated. Finally, we assume that there are p, q = (1, . . ., S)

latent statuses, where p denotes a latent status at time t, and q denotes alatent status at time t + 1.

Let y = (i' J' ,k' ,i" J" ,f(') denote a response vector containing the

possible set of categorical responses to the manifest indicators at time t and

time t + I. Then, for the specific model in question, we define the

proportion of individuals Y generating a particular response y as

s s

prob(Y = y) = LL /)pPi' IpPj' IpPk'lpPrlpPrlpPK'lpTqlp

p-l q-l

(AI)

where Sp is the proportion of individuals in latent status p at time t (see,

e.g., Table 3). The ps are the response probabilities given latent status

van de Pol, F" & de Leeuw, J. (1986). A latent Markov model to correct

for measurement error. Sociological Methods and Research, 15, 118-141.

van de Pol, F., & Langeheine, R. (1989). Mover-stayer models, mixed

Markov models, and the EM algorithm; with an application to labour

market data from the Netherlands Socio-Economic Panel. In R. Coppi &

S. Bolasco (Eds.), Multiway data analysis (pp. 485-495). Amsterdam,the Netherlands: North-Holland.

Vellutino, F. R., & Scanlon, D. M. (2002). The interactive strategies

approach to reading intervention. Contemporary Educational Psychol-

ogy, 27, 573-635.

Vellutino, F. R., Scanlon, D. M., Sipay, E. R., Small, S. G., Pratt, A., Chen,

R., & Denckla, M. B. (1996). Cognitive profiles of difficult-to-remediate

and readily remediated poor readers: Early intervention and experiential

deficits as basic causes of specific reading disability. Journal of Edu-

cational Psychology, 88, 601-638.

Whitehurst, G. J., & Lonigan, C. J. (2002). Emergent literacy: Develop-

ment from prereaders to readers. In S. B. Neuman & D. K. Dickinson

(Eds.), Handbook of early literacy research (pp. 11-29). New York:Guilford Press.

Wiggins, L. M. (1973). Panel analysis. Amsterdam, the Netherlands:Elsevier.

Willett, J. B., & Sayer, A. G. (1994). Using covariance structure analysis

to detect correlates and predictors of individual change over time.

Psychological Bulletin, /16, 363-381.

Xue, Y., & Meisels, S. J. (2004). Early literacy instruction and learning in

kindergarten: Evidence from the Early Childhood Longitudinal Study-

Kindergarten Class of 1998-1999. American Educational ResearchJournal, 41, 191-229.

Appendix

membership (see, e.g., Table 2). Specifically, Pi'lp is the probability ofresponse i (e.g., pass) to Item 1 at time t, given membership in latent status

p; Prlpis the probability of response i to Item 1 at time t + 1 givenmembership in latent status p; Pj'lp is the probability of response j to Item2 at Time 1 given membership in latent status; Pk'ip is the probability ofresponse i (e.g., pass) to Item 3 at time t, given membership in latent status

p; PK'lpis the probability of response i (e.g., pass) to Item 3 at time t + 1,given membership in latent status p. Finally, the transition probability Tqprepresents the probability of membership in latent status q at time t + 1,

given membership in latent status p at time t (Collins & Wugalter, 1992).

These transition probabilities are arrayed in a transition probability matrix

as can be seen in, for example, Table 3. Extensions of the model inEquation Al can be found in, for example, Collins et al.'s (2000) study.

A special case of the model in Equation Al is the latent class model

(Clogg, 1995). Latent class models are applied to cross-sectional data and,

as such, do not yield transition probability values. Moreover, the conceptof a latent status (which is thought to be dynamic) is reduced to a

cross-sectional idea of a latent class. Thus, we introduce a new parameter,

1'c' representing the proportion of individuals in latent class c. Thus, themodel in Equation Al reduces to

c

prob(Y = y) = L 1'cPi'lcPj'lcPk'lc,

c~l

(A2)

where the remaining parameters are defmed as in Equation AI.This model is used in Tables 2 and 4 in which we present the latentclass memberships at each waveseparatelyforthe fullsample(seeTable 3) and by poverty level, respectively.

STAGE-SEQUENTIAL READING TRANSITIONS

We estimated the parameters of the model in Equations Al andA2 in the WinLTA program (Collins, 2002) via the expectationmaximization algorithm (Dempster, Laird, & Rubin, 1977)using afull information maximum likelihood approach to handle missingdata, under the assumption that the missing data are missingcompletely at random or missing at random (Little & Rubin,2002). Model fit is assessed by comparing the observed responseproportions against the response proportions predicted by themodel. A likelihood ratio statistic is obtained that is asymptotically

563

distributed as chi-square. The degrees of freedom are calculated bysubtracting the number of free parameters to be estimated from thetotal number of response patterns that are possible. Finally, theWinLTA program provides a likelihood ratio test of the nullhypothesis that missing data are missing completely at random.

Received May 24, 2004Revision received July 15, 2005

Accepted July 18, 2005 .

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