comparison of nomothetic versus idiographic-oriented...

Multivariate Behavioral Research, 48:175–207, 2013

Copyright © Taylor & Francis Group, LLC

ISSN: 0027-3171 print/1532-7906 online

DOI: 10.1080/00273171.2012.736042

Comparison of Nomothetic VersusIdiographic-Oriented Methods forMaking Predictions About Distal

Outcomes From Time Series Data

Laura Castro-Schilo and Emilio Ferrer

University of California, Davis

We illustrate the idiographic/nomothetic debate by comparing 3 approaches to

using daily self-report data on affect for predicting relationship quality and breakup.

The 3 approaches included (a) the first day in the series of daily data; (b) the mean

and variability of the daily series; and (c) parameters from dynamic factor analysis,

a statistical model that uses all measurement occasions to estimate the structure and

dynamics of the data. Our results indicated that data from the first measurement

occasion does not provide information about the couples’ relationship quality or

breakup 1 to 2 years later. The mean and variability of the time series, however,

were more informative: females’ average positive and negative affect across time

was related to relationship quality, whereas males’ variability in negative affect

across time was predictive of breakup. The dynamic factor analysis, in turn, allowed

us to extract information central to the dyadic dynamics. This information proved

useful to predict relationship quality but not breakup. The importance of examining

intraindividual variability and couple dynamics is highlighted.

In psychological research, it is common practice to administer a series of mea-

sures to a sample of individuals at a single timepoint. These data are then used to

predict important outcomes, which typically are also measured on one instance.

If the interest is on individual processes, however, the validity of findings derived

from such data is questionable. The main assumption in these types of analyses

Correspondence concerning this article should be addressed to Laura Castro-Schilo, Depart-

ment of Psychology, University of California, One Shields Avenue, Davis, CA 95616. E-mail:

[email protected]

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176 CASTRO-SCHILO AND FERRER

is that a snapshot of behavior from a group of people at a particular timepoint

is enough to characterize individual processes. There has been much discussion

about the shortcomings of this so-called nomothetic approach in psychological

research (Epstein, 1994; Hamaker, Dolan, & Molenaar, 2005; Molenaar, 2004;

Nesselroade & Ford, 1985). Particularly, advocates of individual-level analyses

have argued that “for many of the most interesting aspects of humans, multi-

variate, multioccasion, multiperson measurement arrangements are likely to be

essential” (Nesselroade & Ford, 1985, p. 58). This argument rests on the fact

that human behavior is complex, and thus, complex methods must be pursued to

capture such complexity. Other researchers affirm that the trajectories of groups

of individuals are not likely to characterize any particular pattern of intraindi-

vidual variability in the population. For example, Molenaar (2004) proved that

the covariance structure of a one-factor model that has fixed loadings (i.e., same

association between the factor and the corresponding manifest variable for each

individual in the sample) is indistinguishable from that of a one-factor model

with random loadings (i.e., loadings are freely estimated for each individual

in the sample). This implies that the loadings from a one-factor model—with

fixed loadings—might fall far from the loadings that any particular person in

the sample would have, if they had been estimated.

Supporters of an “idiographic” approach to psychological research recognize

the challenge of generalizing the results from an individual-level analysis to

a group of people, and thus, recommend repeated single-subject designs to

gather information that applies to multiple individuals (Jones, 2007; Nessel-

roade & Ford, 1985). One way to investigate the potential benefits of analyses

incorporating multivariate, multioccasion, and multiperson data to the study of

psychological processes is to use empirical data to compare nomothetic versus

idiographic-oriented methods. In doing so, one could identify the degree of

information revealed from each approach.

In this article we focus on models that incorporate data from multiple mea-

surements at multiple timepoints for multiple individuals. The data for these

models consist of daily self-reports from couples involved in romantic relation-

ships. The core questions that we attempt to shed light on are as follows: Can

we predict relationship quality or breakup equally from a one-timepoint assess-

ment compared with a series of daily assessments? Is there an improvement

in our understanding of affective processes and how these lead to relationship

quality and breakup in relationships when we consider multiple timepoints of

measurement?

We begin with a historical discussion of the nomothetic and idiographic

perspectives in psychological research followed by a brief literature review on

relationship quality and dissolution. Then, we describe potential approaches

for making predictions about relevant outcomes (in our example, relationship

quality and breakup). We describe the Dynamic Autoregressive Factor Score

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COMPARISON OF METHODS FOR MAKING PREDICTIONS 177

(DAFS) model, a statistical model tailored to the study of individual-level data.

After detailing our methodology, we compare the results of three different

prediction approaches: (a) using one-timepoint reports of positive and negative

affect as predictors, (b) using the mean and standard deviation of positive and

negative affect of all the available timepoints as predictors, and (c) using the

resulting dynamic parameters from individual-level DAFS models with positive

and negative affect as predictors. Although we apply these models to one unit of

data (i.e., a dyad) at a time, we show an approach to extract the information from

each DAFS model and submit it to a multiple regression analysis as a secondary

step. We consider this third approach “idiographic-oriented” as it considers the

dynamics of each unit across time while also providing group-level estimates

of prediction.1 Moreover, we discuss unresolved issues that arise when using

information from individuals to make inferences about groups. We conclude the

article highlighting the benefits and shortcomings of each approach.

NOMOTHETIC AND IDIOGRAPHIC PERSPECTIVES IN

PSYCHOLOGICAL RESEARCH

In their quest for knowledge of reality, the empirical sciences either seek the

general in the form of the law of nature or the particular in the form of the

historically defined structure. On the one hand, they are concerned with the form

which invariably remains constant. On the other hand, they are concerned with

the unique, immanently defined content of the real event : : : scientific thought

is nomothetic in the former case and idiographic in the latter case. (Windelband,

1894/1980, p. 175)

In his rectorial address at the University of Strasbourg, Windelband (1894/1980),

a German philosopher, first coined the terms nomothetic and idiographic to

refer to the methodologies that different disciplines employed at the time. When

discussing the place of psychology within these alternative perspectives, Windel-

band believed that it fell “unambiguously” within the nomothetic bounds. Stern

(1911) reintroduced the nomothetic and idiographic terms in Germany in an

attempt to organize psychological science around the individual. With a similar

goal, Allport (1937) acquainted American psychologists with the nomothetic

and idiographic terms to encourage the integration of idiographic methodology

into psychological inquiry. The topic was controversial then and continues to

1We purposely use the term idiographic-oriented to indicate that although this approach is based

on modeling the individual unit of analysis, certain assumptions (described in the Discussion section)

about these individual units are made to arrive at group-level estimates. Thus, this third approach is

not idiographic in the purest sense of the word.

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be to the present day. Researchers have taken multiple stands on this issue,

some arguing that idiographic approaches represent “an antiscience point of

view” (Nunnally, 1967, p. 472), others arguing that findings from nomothetic

methods are simply “fundamentally inadequate” (Lamiell, 1981, p. 276) to

inform the understanding of individual experience, and yet others taking a less

extreme position affirm that nomothetic-based knowledge can be used to craft

hypotheses for idiographic research (Runyan, 1983). Kluckhohn and Murray’s

(1953, p. 53) classic statement “Every man [sic] is in certain respects (a) like

all other men, (b) like some other men, (c) like no other man” was quoted by

Runyan (1983) to suggest three levels of inquiry; he argued that personality

psychology was charged with the task of understanding phenomena that apply

to all individuals, to some individuals, and to only one individual. In this sense,

nomothetic and idiographic approaches should be employed synergistically to

advance psychological science.

The nomothetic-idiographic debate is ongoing, as idiographic supporters be-

lieve that the focus in psychology is still primarily nomothetic (e.g., see Mole-

naar, 2004). Although idiographic supporters acknowledge the need for general

laws, one pressing challenge is finding an optimal approach for combining

information from individual-level analyses to make statements about groups of

individuals or to arrive to general laws (however, see Runyan, 1983, who argues

that idiographic research need not generalize to groups of people or universal

laws). Several investigations have focused on this issue, some suggesting individ-

ual replications (Jones, 2007; Nesselroade & Ford, 1985); others have employed

techniques in which several time series are stacked together and analyzed as one

(e.g., Russell, Bryant, & Estrada, 1996) or have pooled time series by identifying

equivalent variance-covariance matrices prior to conducting analyses and creat-

ing subgroups to which generalizations can be made (Nesselroade & Molenaar,

1999); yet others have opted for first carrying out the analyses and then identify-

ing subgroups using cluster analysis (e.g., Hoeppner, Goodwin, Velicer, Mooney,

& Hatsukami, 2008). In this article, we compare idiographic and nomothetic

approaches. We conduct analyses at the dyad level (our unit of analysis) and

take the results from these idiographic analyses to make nomothetic inferences.

The analyses use information from couples’ daily affect and make predictions

about future relationship quality and breakup. To put these analyses into context,

we provide a brief review on romantic relationships quality and dissolution.

AFFECT, RELATIONSHIP QUALITY, AND

DISSOLUTION IN ROMANTIC RELATIONSHIPS

Theoretical accounts of romantic relationships place great emphasis on the

interdependence within dyads (e.g., interdependence theory; Kelley & Thibaut,

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1978). However, a large body of literature on romantic relationships ignores the

fundamental fact that romantic partners are a dynamic, interdependent system

with mutual influences over time. Instead, some work in this area still treats

partners as independent units by examining information from only one individual

and relying on cross-sectional data (Karney & Bradbury, 1995). Moreover,

findings from this body of work have been largely based on nomothetic methods.

Although this methodology might be informative in some way, it disregards

longitudinal processes that occur at the individual or dyadic level.

The contributions of alternative methods (e.g., longitudinal, cross-sectional,

nomothetic, or idiographic) for making predictions about romantic relationships

have not been compared in the past. Specifically, the contribution of dynamic

information—which is gathered from complex models fit to longitudinal data—

has not been compared with other simpler approaches for predicting relevant

outcomes such as relationship quality and dissolution. However, previous work

using different methods does show that positive and negative affect are related to

the quality and stability of romantic relationships (Caughlin, Huston, & Houts,

2000; Ferrer, Steele, & Hsieh, 2012; Kim, Martin, & Martin, 1989; Watson, Hub-

bard, & Wiese, 2000), that positive and negative affective dynamics in romantic

couples are temporally interdependent (Steele & Ferrer, 2011), and that patterns

of intraindividual variability are predictive of future breakup (Ferrer et al., 2012).

In sum, these findings suggest that the dynamics of positive and negative affect

in intimate relationships are predictive of relationship quality and dissolution.

In the current study, we adopt an idiographic-oriented approach for testing this

proposition. Our comparisons are intended to examine whether the time series

of affect from dyads (using means and variability and, separately, using dynamic

information from the time series) are predictive of relationship quality and/or

breakup in the future. In addition, we examine the added predictive value of

considering these longitudinal approaches over one timepoint of measurement.

APPROACHES FOR PREDICTING DISTAL OUTCOMES

When data are taken from multiple individuals at one timepoint, the statistical

models for making predictions are easy to determine. Depending on the number

of variables measured per individual, one might opt for a path analysis with

or without latent variables, or simply a regression model. The results gathered

from any of these statistical methods would represent a nomothetic approach

for making predictions because one parameter would reflect the effect of the

predictor on the outcome for every individual in the analysis. When data are

highly dimensional, on the other hand, the options are not so clear. For example,

Cattell (1946) introduced what he termed the “covariation chart” (also known

as “data box”), which consisted of a three-dimensional space with occasions

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(or time), variables, and persons (or organisms) in each axis (see Figure 1).

He later expanded upon this structure by introducing the Basic Data Relation

Matrix, which comprised a 10-dimensional space with persons, focal stimuli,

response patterns, environmental backgrounds, observers, and five time variants

from each of these (Cattell, 1966). For clarity, we limit our discussion to the

original 3-dimensional covariation chart, as cross-sectional data—which are most

often used in psychological research—consist of multiple variables from multiple

individuals at one timepoint.

The multiple dimensions of Cattell’s (1966) data box illustrate the ana-

lytical options available for testing hypotheses. If one were to collect data

with multiple measurements at multiple timepoints from multiple individuals

(see Figure 1A), then a decision could be made about whether nomothetic or

idiographic inferences are sought. To submit data like those from Figure 1A to

traditional (nomothetic) statistical methods, one would have to ignore one of the

three dimensions or aggregate across one dimension. Thus, depending on the

dimensions that one chooses to maintain or aggregate across, the resulting data

structure could entail multiple variables from one individual taken at multiple

FIGURE 1 Alternative data structures. A) Three-dimensional data structure: multiple

measurements from multiple people at multiple timepoints. B) Two-dimensional data

structure: multiple measurements from one individual at multiple timepoints. C) Two-

dimensional data structure: multiple measurements from multiple people at one timepoint.

D) Two-dimensional data structure: one measurement from multiple individuals at multiple

timepoints.

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timepoints (see Figure 1B), multiple variables taken from multiple people at

one timepoint (see Figure 1C), or one variable from multiple people at multiple

timepoints (see Figure 1D).

Alternatively, multilevel models with time-varying covariates or second-order

latent growth curve models could be applied to the three-dimensional data in

Figure 1A. These analyses fall within nomothetical and idiographic standards

because information about intraindividual and interindividual variability can

be obtained. However, the individual trajectories derived from these models

are pulled toward the group-based trajectory, which can obscure idiosyncratic

patterns in the data. Data such as those depicted in Figure 1B are suited for

idiographic methods, as these methods result in estimates that characterize one

particular individual.

One statistical technique apt for modeling the latter types of data is the

DAFS, which is a time series model that uses latent variables. Other possible

options include time series analysis without latent variables (Box & Jenkins,

1976) and dynamical systems models such as the damped linear oscillator

(Nesselroade & Boker, 1994). As with any other analysis, the choice of model

depends on the theoretical question to answer. Data such as those in Figure

1C are apt for nomothetic methods, with estimates that characterize a group

of people. R-technique factor analysis, general linear models, and generalized

linear models, among others, are techniques that can be applied to these data.

Finally, data such as those shown in Figure 1D could, in theory, be submitted to

nomothetic or idiographic analyses. Most often, these types of data are analyzed

using repeated measures ANOVA or latent growth curve modeling, which are

nomothetic approaches, even though the latter can yield information about both

intraindividual changes and interindividual differences. Also, if only one person

is selected, data such as those in Figure 1D could be analyzed in an idiographic

manner, assuming that enough observations across time are available.

We believe that a compromise between the nomothetic and idiographic ap-

proaches is possible by decomposing a three-dimensional data structure (as in

Figure 1A) into multiple two-dimensional data structures (as in Figure 1B)

and analyzing them with idiographic methods. This alternative is idiographic-

oriented in that dynamics unique to the individual are considered prior to aggre-

gating information across people. In the next section we describe one statistical

technique suited for idiographic analyses, the DAFS.

DYNAMIC AUTOREGRESSIVE FACTOR

SCORE MODEL

In his endeavor to study the structure of intraindividual personality, Cattell sug-

gested the application of the common factor model to time series data from one

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individual (Cattell, Cattell, & Rhymer, 1947). The resulting latent variables from

this analysis represent intraindividual variation of the observed variables. A prob-

lem with this technique, however, is that it does not take into account the lagged

relationships of both observed and latent variables (Anderson, 1963). Lagged re-

lationships are important because they can indicate the degree to which one latent

variable influences another latent variable or observed variables across time.

Acknowledging the limitations of P-technique, the dynamic factor model

was developed in which the lagged covariation among the various repeated

measurements was incorporated into the model. One specification of the dynamic

factor model is the DAFS (Browne & Nesselroade, 2005; Nesselroade, McArdle,

Aggen, & Meyers, 2002). A lag-1 specification of the DAFS in matrix notation

takes the following form:

yt D F˜t C ©t t D 1; 2; : : : ; T

˜t D B˜t�1 C dt ;

where yt is a p � 1 vector of measurements on p variables at time t; F is a

p �q matrix of factor loadings that is invariant over time; ˜t is a q �1 vector of

factor scores at time t ; ©t is a p � 1 vector of unique factors at time t , assuming

©t � N.0; D©/; B is a q �q matrix of regression weights indicating the influence

of the lag-1 common factors on the current factors; and dt is a q � 1 vector

of residuals of ˜t that could not be explained by the lagged effects, assuming

dt � N.0; §/. In this model, common factors are assumed to be uncorrelated

with unique factors. However, unique factors can have an autocorrelational

structure. The ˜t�1 term denotes this is a lag-1 model, but additional lagged

effects can be included. Thus, this model shows that the influences of prior

timepoints take place through the influence of prior factor scores on current

factor scores, which, in turn, influence the current observed variables. Intercepts

are typically not included in the equations because the DAFS is designed to

model the covariations in the data. However, other specifications can account

for trends and nonstationarity (Molenaar, De Gooijer, & Schmitz, 1992).

The DAFS model is a combination of factor analysis and time series analysis.

In the time series literature, there has been discussion about the difficulty

entailed in identifying the appropriate model to fit to time series data (Velicer

& Molenaar, 2013). However, lag-1 models have been advocated as appropriate

for behavioral sciences’ data (Simonton, 1977), and simulation studies have

indeed shown that a lag-1 model provides appropriate results for several different

Auto Regressive Integrated Moving Average processes (Harrop & Velicer, 1985).

In addition, previous analyses with intensive longitudinal data have shown a

lag-1 model is appropriate to characterize daily affective processes (Ferrer &

Nesselroade, 2003; Ferrer & Widaman, 2008). Although these findings suggest

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a lag-1 DAFS model is appropriate for our analyses, we corroborated this

assumption with examination of our empirical data, which we describe later.

We chose to use the DAFS for our idiographic-oriented approach because of

its particular usefulness with data that show consistent fluctuations over time

(Browne & Nesselroade, 2005; Ferrer & Zhang, 2009; Song & Ferrer, 2009).

Also, this model has been extended to examine affective processes in dyads

over time, which allows for the simultaneous investigation of intraindividual and

interindividual variability within the dyad (Ferrer & Nesselroade, 2003; Ferrer

& Widaman, 2008; Song & Ferrer, 2009, 2012). Moreover, the autoregressive

structure of the DAFS is specified at the latent level. That is, the effects of

previous timepoints on future timepoints are modeled with variables that are

free from measurement error. This feature of the DAFS should make this model

preferable over a model that utilizes composite scores instead of latent variables.

To verify this claim, we compared the DAFS with an autoregressive lag-1 (AR1)

model that has observed (i.e., composite) scores instead of latent variables.

Figure 2 shows a lag-1 dyadic DAFS model with one factor and three observed

variables, for two individuals (person A and person B), across measurement oc-

casions t and t C1. In addition to the autoregressive coefficients (i.e., influences

within the same person across time), the model depicts cross-lagged coefficients,

representing the influence of one person on the other across time. The notion

of an autoregressive effect, or lagged effect, has been labeled in the affective

literature as inertia (Kuppens, Allen, & Sheeber, 2010; Suls, Green, & Hillis,

1998). That is, high inertia suggests a strong influence of a variable on itself

from one timepoint to the next. The notion of a cross-lagged effect, on the other

hand, has been conceptualized as reactivity (Suls et al., 1998), for it represents

how reactive one variable is to the influence of another variable across time.

Multilevel models have been employed with daily diary data (similar to

the data used in this investigation) to study, for example, daily intimacy and

disclosure in married couples (Laurenceau, Troy, & Carver, 2005) and to identify

emotional contagion in couples under stress over time (Thompson & Bolger,

1999). These models have attractive features. For example, they do not require

equally spaced data or an equal number of observations across individuals.

Moreover, in a multilevel framework, between-level and within-level parameters

are estimated simultaneously, describing a common trajectory for the sample and

differences in the trajectory across individuals. This feature makes these models

more appealing than repeated measures ANOVA, for which only mean trajecto-

ries are estimated. However, if one is interested in idiographic approaches, these

multilevel models are more limited than models that place all their focus on the

individual (or other unit of interest). The primary reason for this is multilevel

models have assumptions about the variability across individuals; that is, they

assume random effects are normally distributed. As a consequence, if one wanted

to obtain empirical Bayes estimates, individuals’ trajectories would be pushed

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FIGURE 2 Lag-1 dyadic Dynamic Autoregressive Factor Score (DAFS) model with three

observed variables and one factor. Double-headed arrows in the structural model denote

correlations between the latent variable residuals. Although not depicted in this figure,

covariances among unique factors across time and persons are specified.

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toward the group-mean trajectory. The degree of shrinkage toward the fixed

effects would depend on the number of data points for a particular individual

in the sample and the relative difference in ordinary least squares’ estimates of

such individual in comparison with others in the sample.

Although one could avoid getting empirical Bayes estimates by using multi-

level models directly in a one-stage procedure, the assumption of normality of

the parameters is one that persists. On the other hand, purely idiographic models

focus solely on the unit of analysis and its dynamics over time. Parameters from

individually run DAFS models do not have distributional assumptions, and as

such, we can expect more variability in the parameters, which might result in

greater predictive value of distal outcomes. Furthermore, fitting a DAFS model

per dyad allows for unique factorial structures across couples, something that

could not be accommodated in one multilevel model.

Given the aims of our study and the characteristics of our empirical data (i.e.,

dyadic multivariate time series data, described later), the dyadic DAFS seems

ideal for delineating dyadic affective dynamics for each couple over time. We

also investigate whether such dynamics carry unique information about each

couple by using differences in the dynamics across dyads to predict relationship

quality and stability at a later time.

METHOD

Participants and Procedures

Our data are part of a longitudinal project about dyadic interactions. Partic-

ipants are couples who began the study while they were in a premarital or

marital relationship. Advertisements were placed in local newspapers and on

the Internet. Individuals could participate only if their partners participated as

well. During an intake appointment, participants gave informed consent and

completed a questionnaire containing measures related to their relationship,

affect, and demographic questions. Upon completion, participants received daily

diary packets containing questions about their daily emotional experiences. They

were instructed to complete one page each evening for up to 90 days. For our

analyses, we considered those couples that had a minimum of 50 days of daily

data (N D 197 couples). The couples in our subsample ranged in age from 17 to

74 years (M D 25:08, SD D 10:39) and reported having been in the relationship

from 1 month to 54 years (M D 3:39, SD D 6:52).

Measures

Positive and negative affect. All participants were asked to complete

individually a 20-item daily questionnaire about their positive and negative

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affect for up to 90 consecutive days (the Positive and Negative Affect Schedule

[PANAS]; Watson, Clark, & Tellegen, 1988). Participants answered all items in

response to the stem “Indicate to what extent you have felt this way today.”

Each item was rated on a 5-point Likert scale (1 D very slightly or not at all

and 5 D extremely). The reliability estimates (coefficient alpha) of the PA and

NA subscales of the PANAS at the first occasion were .87 and .86 for males

and .85 and .84 for females.

Relationship quality and breakup. Between 1 and 2 years after the initial

visit, couples returned to the laboratory for a follow-up interview about relation-

ship quality and status. If participants indicated they were no longer together with

their previous partners, they were considered broken up. To assess relationship

quality, six items from the Perceived Relationship Quality Component Inventory

(Fletcher, Simpson, & Thomas, 2000) were used. Sample items included “How

satisfied are you with your relationship?” “How committed are you with your

relationship?” and “How intimate are you in your relationship?” These items

were rated on a 7-point Likert scale (1 D not at all and 7 D extremely) and

were averaged into a composite score at the dyad level, resulting in one quality

score per couple. The reliability estimates (coefficient alpha) of the relationship

quality scale were .92 for females and .95 for males.

Data Analysis

We proposed three approaches for making predictions about relationship quality

and breakup from the affective data. In the first approach, we used information

from one measurement occasion. We computed composite scores of PA and

NA based on the PANAS reports from the first day of data collection and

used these as predictors of relationship quality and breakup. This approach

consisted of just using the scores collected on the first measurement occasion

for prediction, unlike the second and third approaches (described later), which

used information from all measurement occasions, and as such, might capitalize

on having higher reliability.2 In an attempt to further evaluate the first approach

in a way not biased by its potential lower reliability, we used the estimated

internal consistency (coefficient alpha) of the two PANAS subscales, separately

for males and females, to correct each predictor for the effects of measurement

error. This correction was performed by fixing the residual variance of each

first-occasion predictor at (1 � reliability) � predictor variance.

2The interpretation of the first measurement occasion variables as having lower reliability is

arguable (see Hertzog & Nesselroade, 1987) because in our case these variables are a measure of

state affect, which might be highly variable across time (suggesting low test-retest reliability) but

can have high internal consistency.

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In the second approach, we incorporated data from the entire time series (from

50 to 90 days of measurement) for each couple by computing the mean PA and

NA as well as the standard deviation of PA and NA across all daily reports.

Then, we used the mean and standard deviation of each individual in the couple

as predictors of relationship quality and breakup. The standard deviation was

used to represent the variability in affect for each individual within the couple.

Using the standard deviation for this purpose has been shown to yield meaningful

results (e.g., Eid & Diener, 1999).

In the third approach, we also considered all of the time series but we

modeled the dynamics across time for each individual couple using a lag-1

dyadic DAFS model with two factors (i.e., PA and NA) per person. We chose

a lag-1 model based on the time series literature mentioned before but also

based on empirical evidence gathered from examination of the linearly detrended

time series’ autocorrelation function (ACF) and partial autocorrelation function

(PACF) plots. We selected a random sample of 20 dyads, computed composite

scores of their positive and negative affect detrended time series, and plotted

their ACF and PACF.3 For the most part, the plots suggested a lag-1 or no-lag

model. We chose a lag-1 model as an approximation model that could be fit to

all dyads, although in very few instances (5 out of the 80 time series) the ACF

and PACF plots pointed to a lag-2 model. Inspection of the ACF and PACF plots

also suggested stationarity.

To reduce the number of observed variables in the DAFS model and improve

the psychometric properties of the factors, we grouped the PANAS items to

create a total of six parcels (Kishton & Widaman, 1994), three representing

positive affect (PA) and three for negative affect (NA).4 We used these parcels

as observed indicators of PA and NA in the dyadic DAFS. To identify the model,

we set the variance (or residual variance in the case of endogenous factors) of

the latent variables to unity.

We carried out the DAFS analyses by running Mplus (Muthén & Muthén,

2010) in batch mode through R (R Development Core Team, 2010). That is,

we ran 197 dyadic DAFS models in Mplus and extracted all the standardized

dynamic parameters (i.e., the autoregressive and cross-lagged standardized esti-

mates, 16 in total) from the models using R. These parameters represented all

possible influences of PA and NA between the 2 individuals in the couples. For

example, a female’s PA on a particular day could have an influence on her own

3ACF and PACF plots are available from Laura Castro-Schilo upon request.4The parcels for positive affect were created in the following fashion: Parcel 1 D enthuse,

interest, strong. Parcel 2 D excited, determined, attentive. Parcel 3 D proud, inspired, alert, active.

For negative affect: Parcel 1 D afraid, irritable, hostile. Parcel 2 D distress, nervous, ashamed.

Parcel 3 D upset, scared, guilty, jittery. The assignment of items across parcels was based on the

domain-representative method for parcel construction put forth by Kishton and Widaman (1994) and

entailed factor analyses at the group level.

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PA the day after (i.e., lagged/autoregressive parameters) and on her own NA the

day after (i.e., cross-lagged parameters within a partner). Similarly, her PA on a

particular day could influence her male partner’s PA and NA the following day

(i.e., cross-lagged parameters across partners). The standardized estimates were

saved in a separate data set, which also included the variables from the first and

second approach, and information about the couple’s status (together or broken

up) and relationship quality (the average across both partners). Finally, we used

these dynamic parameters from each couple in the third approach as predictors

of relationship quality and breakup.

Because our goal was to compare the information gathered by each of the

three proposed approaches, we used the structural equation modeling framework

to run regression models, place restrictions on parameters of interest, and conduct

Wald chi-square tests. Models were run in Mplus (Muthén & Muthén, 2010)

and missing data were handled with multiple imputation using the Bayesian

estimator, which employs the Markov Chain Monte Carlo algorithm based on

the Gibbs sampler (Asparouhov & Muthén, 2010a). Missing data were present

in the outcome measures (see Table 1) and, to a lesser extent, in the predictors

from the DAFS models (10 cases were missing). We chose multiple imputation

over other approaches, such as Full Information Maximum Likelihood (FIML),

TABLE 1

Descriptive Statistics for the First Timepoint Score, Mean and Variability of Time Series

Variables N M SD Min Max

First timepoint

Males’ PA 197 2.87 0.74 1.00 4.89

Females’ PA 197 2.74 0.69 1.11 4.33

Males’ NA 197 1.72 0.67 1.00 4.67

Females’ NA 197 1.74 0.63 1.00 3.92

Mean and variability of time series

Mean of males’ PA 197 2.81 0.64 1.47 4.93

Mean of females’ PA 197 2.63 0.61 1.22 4.41

Mean of males’ NA 197 1.52 0.33 1.02 2.84

Mean of females’ NA 197 1.51 0.31 1.04 2.63

SD of males’ PA 197 0.55 0.17 0.15 1.12

SD of females’ PA 197 0.57 0.16 0.22 1.27

SD of males’ NA 197 0.43 0.17 0.07 0.96

SD of females’ NA 197 0.45 0.18 0.09 1.16

Variables at follow-up

Relationship quality 139 5.88 0.90 3.08 7.00

Breakup 153 0.23 0.42 0.00 1.00

Note. PA D positive affect; NA D negative affect. Each PANAS item was measured on a

5-point Likert scale where 1 D very slightly or not at all and 5 D extremely.

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because FIML was more computationally intensive, particularly for the models

with the categorical outcome (i.e., breakup). We imputed 10 data sets from

an unrestricted variance covariance model using all relevant variables (i.e.,

all predictors and both outcomes). Parameter estimates from the models were

averaged across replications, and standard errors computed according to Rubin’s

rules (1987). The Wald chi-square tests were performed using the estimated

asymptotic variance of the parameters (for technical details see Asparouhov &

Muthén, 2010b).

In the first model, we specified the respective outcome (relationship quality

or breakup) as a function of males’ and females’ PA and NA from the first

measurement occasion. To assess the overall predictive value of these first-

occasion predictors, we compared a model in which all predictors had an effect

on the outcome with one in which these predictions were fixed to zero. Following

the same logic, we specified a second model with the first-occasion predictors

together with the mean and variability of the time series as predictors (i.e., pre-

dictors from the second approach). Effects from this latter model were compared

with an alternative model in which the effects of the second approach predictors

on the outcome were fixed to zero. Finally, we assessed the overall predictive

value of the dynamic parameters by fitting a model in which predictors from

all three approaches were specified to relate to the corresponding outcome and

compared it to a model with the dynamic parameters fixed to zero.

Rescaling of variables. To facilitate interpretation of the intercept in our

models, we rescaled the predictors. In the case of the first measurement occasion,

we subtracted 1 from every value, resulting in values that ranged from 0–4

instead of the original 1–5. The mean and variability for the second approach

were rescaled in two different ways: (a) the mean of males’ and females’ PA

and NA were rescaled such that a value of zero represented the lowest possible

level of PA and NA, and (b) the standard deviations of males’ and females’ PA

and NA were centered such that a value of zero represented the average amount

of variability across the sample. There was no need to rescale the dynamic

predictors from the DAFS as a meaningful zero already existed in the data: a

lack of affective influence.

RESULTS

Descriptive Statistics

Table 1 lists the sample size, mean, standard deviation, minimum, and maximum

of the PA and NA scores from the first day of data collection; the means and

standard deviations of individuals’ PA and NA across all days of data collection;

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and descriptives of relationship quality and breakup. The means of the variables

at the first timepoint show that couples reported experiencing higher levels of

PA than NA on the first day of the study, and the standard deviation suggests

more variability of PA than NA. The average of the entire time series shows a

similar pattern, with slightly lower mean scores of PA and NA than on the first

day.

With regard to the outcomes at follow-up, relationship quality and breakup

were negatively correlated, rpb.136/ D �:30, p < :001, suggesting lower

relationship quality for those who are more likely to break apart. Relationship

quality data were missing from 58 couples and breakup data were missing from

44 couples. We obtained relationship quality data from some of the couples who

reported breaking up, as 21 couples notified us of their breakup after having

visited our lab for their follow-up, on which they filled out the relationship

quality questionnaire. These data were included in all our analyses. As it would

be expected, the incidence of breakup is not as high as that of staying together

(35 couples reported breaking up), and relationship quality is higher than the

middle of the scale (M D 5:88 in a 1–7 scale).

Dynamic Factor Analysis

Of the 197 DAFS models, 187 converged to a stable solution with estimates

within the accepted boundary space. Descriptive statistics for the 16 dynamic

parameters are listed in Table 2. As in previous work (Ferrer & Widaman,

2008), these parameters show ample variability across individuals. Estimates

representing within-affect autoregressive parameters (e.g., males’ positive affect

regressed on their own positive affect) are positive, with means ranging from

.17 to .20, whereas means for other estimates are close to zero. Overall, the

fit of the models is generally acceptable, with CFIs ranging from .61 to 1.00

.M D :91/ and RMSEAs from 0 to .16 .M D :07/.

Zero-order correlations between our outcomes of interest and the predictors

from all three approaches are presented in Table 3. Based on these coefficients,

the mean of females’ NA, the variability in males’ and females’ NA, and

the day-to-day influences of females’ NA to males’ and females’ NA, males’

PA to females’ PA and males’ NA to females’ PA are significantly related to

relationship dissolution up to 2 years later. The mean of females’ PA and the

day-to-day influences of females’ NA to females’ PA and males’ NA to females’

NA are significantly related to relationship quality.

Model 1: First Measurement Occasion

The predictors from the first regression model did not explain a significant

amount of variability in relationship quality, R2D :02, p D :43. The Wald test

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TABLE 2

Descriptive Statistics of Parameters From DAFS Models

Variables M SD Min Max

Fit indices

CFI 0.91 0.06 0.61 1.00

RMSEA 0.07 0.03 0.00 0.16

Lagged relations

Males’ PA ! Males’ PA 0.20 0.22 �0.57 0.70

Males’ NA ! Males’ NA 0.18 0.23 �0.37 0.78

Females’ PA ! Females’ PA 0.18 0.20 �0.36 0.61

Females’ NA ! Females’ NA 0.17 0.20 �0.44 0.69

Cross-lagged relations within partners

Males’ NA ! Males’ PA 0.00 0.20 �0.74 0.56

Males’ PA ! Males’ NA �0.01 0.22 �0.65 0.60

Females’ NA ! Females’ PA �0.01 0.18 �0.55 0.42

Females’ PA ! Females’ NA �0.01 0.18 �0.64 0.48

Cross-lagged relations across partners

Males’ PA ! Females’ PA 0.03 0.20 �0.38 0.92

Males’ NA ! Females’ PA 0.01 0.20 �0.42 0.86

Males’ PA ! Females’ NA �0.03 0.18 �0.54 0.43

Males’ NA ! Females’ NA 0.01 0.20 �0.50 0.54

Females’ PA ! Males’ PA 0.01 0.19 �0.55 0.75

Females’ NA ! Males’ PA �0.02 0.19 �0.55 0.85

Females’ PA ! Males’ NA 0.00 0.17 �0.51 0.57

Females’ NA ! Males’ NA 0.03 0.19 �0.60 0.74

Note. PA D positive affect; NA D negative affect. Each variable represents a vector of

regression weights from the Direct Autoregressive Factor Score (DAFS) (e.g., Males’ NA ! Males’

PA D males’ positive affect regressed on males’ negative affect). Descriptives are based on the

standardized DAFS parameters.

revealed that fixing the first measurement occasion predictors to zero did not

worsen the model fit, �¦2.4/ D 0:72, p D :95. Thus, reports of PA and NA

on the first day of the study were not predictive of couples’ future relationship

quality.

We followed the same procedure to investigate whether a single measurement

of PA and NA was predictive of couples’ relationship status (i.e., together,

breakup) in the future. Results from the first model for breakup suggested that

the PA and NA from the first occasion of measurement did not significantly

predict breakup, �¦2.4/ D 1:52, p D :82. We proceeded to run two additional

models correcting the first occasion predictors for measurement error. The results

from the latter analyses were nearly identical to the previous results. Thus,

regardless of measurement error, the first assessment of affect was not predictive

of relationship quality or breakup.

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Model 2: Mean and Variability of Time Series

In the next step, we focused on the mean and standard deviation of PA and

NA from each individual’s entire time series. When these variables entered

the prediction of relationship quality together with the first-time variables, the

Wald chi-square test indicated an overall predictive value, �¦2.8/ D 26:19,

p < :01. The first timepoint predictors, together with the mean and standard

deviation of the time series, explained 15% of the variance in relationship quality

.R2D :15; p < :01/. The regression coefficients from this analysis are presented

in Table 4. The model’s intercept indicates that the average level of relationship

quality reported by those couples with the lowest levels of PA and NA—in

the first occasion and across the time series—and with average variability of

affect across their time series, was 5.56 out of a possible 7. This suggests that

couples with low levels of PA and NA, and average variability in their PA and

NA, reported a relatively high level of relationship quality. Relationship quality

increased significantly, b D 0:54, SE D 0:15, p < :01, for every unit increase in

the mean of the females’ PA time series and decreased significantly, b D �0:91,

SE D 0:40, p < :05, for every unit increase in the mean of the females’ NA time

series. These results suggest that females’ mean PA and mean NA of a 3-month

span are related to relationship quality 1 to 2 years later. Analyses adjusting for

measurement error in the first set of predictors were nearly identical.

TABLE 4

Regression Coefficients From the Prediction of Relationship Quality

Based on the First Occasion and the Mean and

Variability of the Time Series

Predictors of

Relationship Quality b SE t P

Intercept 5.56 0.40 13.98 < .01

1st time males’ PA 0.07 0.11 0.58 0.56

1st time females’ PA �0.11 0.11 �0.99 0.32

1st time males’ NA 0.10 0.13 0.74 0.46

1st time females’ NA 0.07 0.14 0.50 0.62

Mean of males’ PA �0.10 0.15 �0.67 0.50

Mean of females’ PA 0.54 0.15 3.57 < .01

Mean of males’ NA 0.05 0.39 0.13 0.90

Mean of females’ NA �0.91 0.40 �2.26 < .05

SD of males’ PA 0.32 0.52 0.62 0.54

SD of females’ PA �0.76 0.54 �1.42 0.16

SD of males’ NA �0.06 0.73 �0.09 0.93

SD of Females’ NA 1.15 0.71 1.62 0.11

R2

D :15

Note. PA D positive affect; NA D negative affect.

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Next, we investigated the unique contribution of the mean and variability of

the time series to predict relationship breakup using logistic regression. As be-

fore, the model was specified so the predictors from the first and second approach

had freely estimated predictive parameters, and a Wald test compared this model

against one in which the predictors from the second approach were fixed to zero.

The test indicated a significant unique contribution for the prediction of breakup

from the mean and variability of the time series, �¦2.8/ D 20:06, p < :05.

The resulting regression weights (in log-odds) and odds ratios are presented in

Table 5. The single significant predictor of breakup was the variability in males’

NA across the time series, b D 5:66, SE D 2:27, p < :05. The odds ratio for

this parameter suggests that, for every unit increase in the standard deviation of

males’ NA across time, the odds of breaking up (vs. staying together) increase

by a factor of 288. However, one unit increase in the standard deviation is

not within the possible values of our data (the mean-centered variable in our

sample has a maximum value of 0.53). Dividing the regression weight in half

and exponentiating it results in the odds ratio for a half unit increase, which is

17. Thus, the odds of breaking up increase by a factor of 17 for those males who

go from having an average amount of variability in NA to having the maximum

amount of variability in NA in our sample. Results from the analysis correcting

for measurement error in the first-occasion predictors were very similar. In sum,

the second set of predictors had a significant contribution for predicting breakup.

TABLE 5

Regression Coefficients and Odds Ratios From the Prediction of Breakup Based on the

First Occasion and the Mean and Variability of the Time Series

Predictors of

Breakup b SE t p

Odds

Ratio

Intercept 0.34 1.20 0.29 0.78 1.40

1st time males’ PA 0.12 0.34 0.36 0.72 1.13

1st time females’ PA 0.29 0.37 0.77 0.44 1.33

1st time males’ NA �0.17 0.35 �0.47 0.64 0.85

1st time females’ NA 0.04 0.42 0.09 0.93 1.04

Mean of males’ PA �0.22 0.46 �0.47 0.64 0.81

Mean of females’ PA �0.69 0.53 �1.29 0.20 0.50

Mean of males’ NA �2.08 1.26 �1.65 0.10 0.13

Mean of females’ NA 1.71 1.23 1.40 0.16 5.52

SD of males’ PA �2.80 1.60 �1.75 0.08 0.06

SD of females’ PA 0.91 1.70 0.54 0.59 2.48

SD of males’ NA 5.66 2.27 2.49 < .05 288.01

SD of Females’ NA �0.08 2.36 �0.03 0.97 0.92

Note. PA D positive affect; NA D negative affect. Dependent variable was coded 0 D staying

together, 1 D breakup.

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Model 3: Dynamic Parameters from DAFS

In the third set of analyses we used the dynamic coefficients (i.e., autoregressive

and cross-lagged parameters) from the DAFS models as additional predictors

of relationship quality and breakup. For relationship quality, The Wald test

yielded a �¦2.16/ D 60:40, p < :01, pointing to a unique contribution of

the dynamic parameters. The predictors in this model (i.e., first-occasion affect,

mean and standard deviation of affect from the time series, and affective dynamic

parameters from DAFS) explained 39% of the variance in relationship quality

.R2D :39; p < :01/. Thus, these dynamic parameters predicted an additional

24% of variance in relationship quality.

Regression coefficients for this model are presented in Table 6. These results

indicate that the influences of males’ PA and NA on their own NA, from

one day to the next, are important predictors of relationship quality. Similarly,

females’ NA influence on their own PA from one day to the next is an important

predictor of relationship quality. Furthermore, the mean of females’ PA remained

significant. The intercept indicates that when all predictors were zero, the mean

level of relationship quality was 5.62. For every unit increase in the influence

from males’ PA and NA to their own NA, the level of relationship quality

increased and decreased, respectively, b D 0:84, �1.08, SE D 0:36, 0.35,

p < :05. Controlling for all other predictors in the model, a unit increase in the

influence of females’ NA to their own PA resulted in an increase of relationship

quality. On the other hand, a unit increase in the mean of females’ PA throughout

the time series boosted relationship quality, b D 0:53, SE D 0:15, p < :01.

Results from a model with correction for measurement error in the predictors

from the first occasion were nearly identical to the results without correction.

Taken together, these analyses indicate that the affective influences that males

and females exert on themselves are central to the couples’ relationship quality.

In the last set of analyses we used the same dynamic parameters from the

DAFS models as additional predictors of breakup in a logistic regression model.

As before, these new predictors were added to the model with the predictors from

the two previous approaches. The Wald test examining the unique contribution

of the newly added parameters was nonsignificant, �¦2.16/ D 16:80, p D :40.

According to this model, the dynamic parameters are not important predictors of

breakup 1 to 2 years later. Correcting the first measurement occasion predictors

for measurement error did not change the results.

The DAFS model has a measurement model and a structural model in which

the autoregressive and cross-lagged relations are estimated. An alternative, sim-

pler model could be fitted by removing the measurement model and using

composite scores as observed variables. To the degree that measurement error is

present in the observed variables, this new AR1 model should obscure relations

in the data. To test this hypothesis, we fitted such AR1 model and compared its

predictive value with that of the DAFS model.

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TABLE 6

Regression Coefficients From the Prediction of Relationship Quality Based

on the First Occasion, the Mean and Variability of the

Time Series, and the DAFS Parameters

Predictors of

Relationship Quality b SE t P

Intercept 5.62 0.42 13.5 < .01

1st time males’ PA 0.08 0.11 0.78 0.44

1st time females’ PA �0.14 0.10 �1.35 0.18

1st time males’ NA 0.22 0.13 1.70 0.09

1st time females’ NA 0.01 0.14 0.05 0.96

Mean of males’ PA �0.11 0.15 �0.72 0.48

Mean of females’ PA 0.53 0.15 3.53 < .01

Mean of males’ NA �0.17 0.40 �0.44 0.66

Mean of females’ NA �0.54 0.38 �1.43 0.15

SD of males’ PA �0.14 0.46 �0.30 0.76

SD of females’ PA �0.52 0.53 �0.98 0.33

SD of males’ NA 0.07 0.70 0.10 0.92

SD of females’ NA 1.02 0.67 1.53 0.13

Males’ PA ! Males’ PA 0.61 0.38 1.60 0.11

Males’ NA ! Males’ NA �1.08 0.35 �3.08 < .01

Females’ PA ! Females’ PA 0.00 0.38 0.00 1.00

Females’ NA ! Females’ NA �0.11 0.35 �0.30 0.76

Males’ NA ! Males’ PA �0.77 0.43 �1.81 0.07

Males’ PA ! Males’ NA 0.84 0.36 2.34 < .05

Females’ NA ! Females’ PA 1.11 0.37 2.97 < .01

Females’ PA ! Females’ NA �0.54 0.40 �1.33 0.18

Males’ PA ! Females’ PA 0.19 0.39 0.49 0.62

Males’ NA ! Females’ PA �0.71 0.40 �1.81 0.07

Males’ PA ! Females’ NA �0.78 0.42 �1.83 0.07

Males’ NA ! Females’ NA �0.59 0.38 �1.56 0.12

Females’ PA ! Males’ PA 0.21 0.38 0.56 0.58

Females’ NA ! Males’ PA �0.02 0.38 �0.07 0.95

Females’ PA ! Males’ NA �0.39 0.48 �0.80 0.43

Females’ NA ! Males’ NA �0.53 0.44 �1.21 0.23

R2

D :39

Note. DAFS D Direct Autoregressive Factor Score; PA D positive affect;

NA D negative affect.

Results from using AR1 estimates to predict relationship quality were similar

to those with the DAFS model. For relationship quality, the Wald chi-square

test indicated that the dynamic predictors explained a significant amount of

unique variance in relationship quality, R2D :39, p < :01, �¦2.16/ D 51:79,

p < :01. Resulting regression coefficients were in the same direction and close

to the same magnitude from those of the DAFS model, suggesting negligible

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differences between the DAFS and AR1 models. With regard to the prediction

of breakup, results were nearly identical to those with the DAFS parameters.

Adding predictors from the AR1 model did not help explain a significant amount

of variance in breakup above and beyond the variance explained by the predictors

from the first two approaches, �¦2.16/ D 17:91, p D :33.

DISCUSSION

Summary of Results and Theoretical Implications

In this article we examined different approaches for characterizing multivariate

data of psychological processes and compared their use for making predictions

of future outcomes. To illustrate the use of these approaches, we used empirical

data consisting of multiple variables collected at multiple timepoints for multiple

individuals in couples.

In our first approach, we used data from the first measurement occasion

only. The results of these analyses show that this information does not provide

information about the couples’ relationship quality or whether couples are likely

to break up 1 to 2 years later. Thus, although one-timepoint assessments have

economical and other practical advantages, in this context, they do not seem to be

informative. Second, we considered the unique contribution of means and stan-

dard deviations from the entire time series for each individual. The results with

these statistics were more informative than those from the first approach. The

mean and variability of the time series explained a significant amount of unique

variance in our outcomes. Females’ average PA and NA across time play a central

role in predicting relationship quality 1 to 2 years later and variability in males’

NA across time was predictive of breaking up. Moreover, couples in which males

experienced high ups and downs in NA across time were 17 times more likely

to break up than those couples in which males showed little variability in NA.

In the third approach, we used the dynamic parameters from DAFS models

fitted to each dyad separately. These parameters also explained an additional

unique amount of variance above and beyond the variance explained by the first

occasion and mean and variability predictors but only for relationship quality.

Results from these analyses indicate that the daily dynamics are quite informative

about future relationship quality but not breakup. Thus, the affective dynamics

revealed by the dynamic parameters seem to reflect a degree of emotional quality

in the relationship but not the mechanisms underlying relationship dissolution.

Decisions to terminate a relationship might be linked to a large shock to the

system or to effects that build up over time until some rupture point. In either

case, these effects would not be captured by the DAFS model, which was

specified to capture daily fluctuations in affect in a stationary way.

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Some important aspects of our analyses deserve mentioning. For example, the

affective inertia (i.e., influences in affect from one day to the next) manifested by

males’ NA was predictive of lower perceived relationship quality at the couple

level. Also, the reactivity showed by males’ NA in response to their own PA was

positively related to relationship quality and so was the reactivity of females’

PA to their own NA. These parameters representing reactivity of PA and NA

are challenging to interpret as increases in NA would not be hypothesized to

predict higher relationship quality. Furthermore, the zero-order correlations be-

tween these parameters and relationship quality are r.131/ D :01, p D :94 and

r.131/ D :24, p < :01 for males and females, respectively. For females, one

could argue that increases in NA lead to higher PA, which could result in higher

relationship quality. However, this argument does not apply to males, for whom the

correlation between their parameter and the outcome reflects a suppression effect.

One complexity in understanding the dynamic effects arises from the large

number of predictors in the regressions. One must keep in mind that the effects

exist in the context of all predictors in the model. Thus, the three aforementioned

dynamic parameters are significant after adjusting for the first timepoint of

measurement, mean, and variability of the time series.

Also interesting is that coupled dynamic effects between males and females

were predictive of relationship quality at the .10 level. Presumably, some of

these parameters would reach conventional criteria for statistical significance if

we had not controlled for the effects of the predictors from the first and second

approaches. Although the inclusion of a large number of predictors creates a

challenge for the interpretation of results, our goal was to assess the overall

contribution of each set of predictors to explaining variability in the outcomes.

The detrimental effects of negative affective influences, within and between

partners, in the success of romantic relationships have been hypothesized in the-

oretical work (Lindahl & Markman, 1990; Markman, 1991) and some evidence

of this exists (Levenson & Gottman, 1983). Our results show further empirical

support for this notion. Females’ consistent experience of NA across time seems

to harm relationship quality, but their experience of NA on a given day might

result in higher PA the following day, and this pattern could boost relationship

quality. Arguably, this description of emotional ups and downs might depict

women who are high in neuroticism, a characteristic thought to pose a challenge

for successful romantic relationships (Karney & Bradbury, 1995). Thus, future

research should investigate if there is any value of experiencing NA for females.

With regard to breakup, the mean and variability of PA and NA across time

revealed useful information about the status of the relationship 1 to 2 years later.

But unlike for relationship quality, this pattern was not found when using the

dynamic parameters from the DAFS model (although several of the dynamic

parameters had significant zero-order correlations with breakup). This is an

insightful finding as it suggests that, once males’ variability in NA is accounted

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for, day-to-day affective dynamics are not determinants of relationship status.

Rather, the overall mood swings in NA across time (particularly for males)

play a central role with regard to relationship dissolution. Thus, for relationship

dissolution, our results also supported previous hypotheses of harmful effects

of negative influences in affect within partners (Levenson & Gottman, 1983;

Lindahl & Markman, 1990; Markman, 1991).

Our findings shed light on several aspects of the close relationships’ literature.

First, the DAFS model stays true to theoretical accounts of romantic relationships

that stress the interconnectedness of individuals in a couple (e.g., Gottman,

Murray, Swanson, Tyson, & Swanson, 2002; Kelley & Thibaut, 1978). The

dynamic parameters in the DAFS model characterize the interdependence of

the dyad, which is a main advantage of using this method, that is, matching

theory with appropriate statistical models. Also, this investigation joins the scarce

literature that considers information from both partners in a relationship and

collects data at more than one point in time. Investigations have suggested gender

differences in relationship conflict management; particularly, males appear to

struggle more than females in handling conflict (Baucom, Notarius, Burnett, &

Haefner, 1990). This might help explain why inertia in males’ NA, but not in

females’, was related to relationship quality.

Methodological Considerations and Limitations

A number of methodological aspects in our analyses deserve discussion. The

mean and variability of the time series proved to be useful predictors of re-

lationship quality and breakup, but the DAFS parameters were only related to

relationship quality. Thus, researchers must consider the differences in informa-

tion provided by these two sets of predictors to assess which approach might

be best for their specific application. The mean of the time series describes the

average affective level of an individual across time. This average affect might

or might not be experienced often throughout the measurement period. The

variability of the time series portrays the degree to which an individual deviates

from that level of affect; high variability suggests an individual who exhibited

large fluctuations around the average level, whereas low variability suggests an

individual who experienced levels of affect close to the average throughout the

assessments. In this regard, the mean and variability of the time series together

are indicative of intraindividual variability.

On the other hand, the dynamic parameters from the DAFS also describe

intraindividual variability but in a different way. Parameters representing within-

person influences suggest the amount of affective inertia an individual has from

one day to the next. A high degree of inertia may typify a person who ruminates

over negative experiences, or savors positive experiences, over time. Conversely,

low inertia could represent an individual who “lives in the present,” for whom

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emotions do not linger from day to day. The cross-lagged parameters represent

reactivity of a state from another state. For example, females’ PA might be

reactive to their NA if their PA is increased or decreased by their NA. As

seen here, the information gathered from the DAFS parameters is very different

from the information gathered from the mean and variability of the time series.

Our results suggest that both pieces of information are differentially useful

for explaining future outcomes and, as such, researchers might consider both

approaches depending on their goals.

Another methodological issue is related to the reliability of the measures. The

predictors from the first occasion of measurement could be interpreted as having

limited reliability (when compared with the predictors from the alternative ap-

proaches) due to the mere fact that they were gathered at a single timepoint (but

see Footnote 2). The predictors included in the additional approaches, in contrast,

capitalized on the reliability of having measured the construct at multiple (up to

90) occasions. Ordinary least squares regression and logistic regression assume

error-free predictors. As such, improvements in a regression model can result

from including predictors that serve as indicators of the reliability of other

variables in the model. In our application, including the standard deviation of the

time series as a predictor of relationship quality and breakup could have served

this purpose as the standard deviation has a direct relationship with the standard

error of the mean. With this in mind, one must question whether the predictive

value of the mean and variability of the time series and the dynamic parameters

from the DAFS is due to the consideration of intraindividual variability itself

or simply due to inclusion of information about reliability in the models. We

argue that reliability is not the reason the DAFS parameters and the mean and

variability are useful predictors of relationship quality and breakup, respectively,

because after adjusting the first-occasion predictors for measurement error we

still found no predictive value of the first-occasion predictors.

In addition, using the AR1 parameters instead of the DAFS parameters did

not change the pattern of results in our regressions, suggesting that both sets

of parameters have similar predictive value. This is likely the case because the

indicators in the DAFS model were parcels. Parcels result in higher factor load-

ings than do individual items (Kishton & Widaman, 1995). Indeed, standardized

factor loadings across dyads fluctuated around .85 and the AR1 model assumes

a constraint of unit weights for all indicators to create a composite score. In sum,

researchers should consider the degree of unique variance across indicators to

decide whether an AR1 model is sufficient for the data.

Importantly, we refer to the DAFS approach as “idiographic-oriented” because

our analyses assume that a lag-1 model is appropriate for all the couples’ time

series. Simulation studies and other investigations suggest a lag-1 model is

appropriate for our data (Ferrer & Nesselroade, 2003; Harrop & Velicer, 1985).

Our empirical examinations of the data also pointed to a lag-1 model for most

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couples. However, to the degree that a lag-1 model fails to characterize the

couples’ dynamics, our results would depart from a true idiographic approach.

One possible limitation of our work is related to our approach of taking

parameter estimates from each individual DAFS model and using them as

predictors of between-dyad differences. The parameter estimates from these

models have standard errors, indicating precision in their estimation. This infor-

mation was not considered in our regression models, which could be particularly

important because of the differences in length of the time series. Moreover, we

extracted the standardized parameter estimates for our secondary regressions.

Although we chose these estimates to facilitate comparability of the parameters

across dyads, the comparability relies on the assumption of equal variances in

the PA and NA factors for all dyads, which might not be tenable. Also related

to this challenge is the comparability of regression weights given the lack of

factorial invariance in the measurement models across dyads. Although some

experts might perceive this as a limitation (because arguably, the same construct

is not being measured for all dyads), others (Nesselroade, Gerstorf, Hardy, &

Ram, 2007) advocate for these idiosyncrasies at the measurement level with

the intention of finding conceptual similarities across people at an abstract level.

Indeed, allowing dyads to have their own factorial structures might be a strength

of our approach. Future work should assess whether or not this is the case. If

factorial invariance across units is the goal, an alternative approach could entail

identifying subgroups of people with similar factorial and dynamic structures;

then comparisons between subgroups could be performed.

Additionally, it is important to consider that our set of predictors coming from

a strictly nomothetic perspective (i.e., the first occasion of measurement) might

not be a completely accurate representation of variables gathered by nomothetic

researchers. That is, the report of PA and NA at the first occasion was based on

a state-like measure. The instructions for answering the PANAS read “to what

extent have you felt this way today” rather than a trait measure that would have

asked about the PA and NA “in general.” Thus, our results might have been

different if we had used a trait measure of affect at the first occasion. Although,

intuitively, it is possible that a trait measure would be highly correlated with

the mean of the time series (and thus might be predictive of distal outcomes),

it is also possible that it would not be strongly related as well-known cognitive

biases (such as fading affect bias and the focusing effect or focusing illusion

bias; Walker, Skowronski, & Thompson, 2003) exist and play a role in the report

of overall affect.

In sum, there are many methodological issues that must be considered when

implementing idiographic-oriented techniques for understanding psychological

processes. At multiple points in time one must make decisions about how to

consider idiosyncratic details, such as identifying the best dynamic models,

the most appropriate factorial structures (constrained or freely estimated across

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dyads), and the most appropriate parameters (with consideration of standard

errors) to extract if secondary analyses are to be conducted. There is not a

clear road map for what steps are most favorable, so aside from proposing

one alternative, we hope in this article we rekindle the nomothetic-idiographic

discussion to bring attention to the challenges associated with making inferences

about groups that also characterize individuals.

SUMMARY

The results from different approaches to making predictions shed light on the

importance of considering longitudinal data, particularly, time series data from

multiple individuals. Naturally, we do not expect that our results will apply to

each couple in our sample. But we believe that our second and third approaches

are better alternatives to classic nomothetic methods because they build psy-

chological science from the ground up. Researchers have discussed ways for

drawing inferences about groups based on individual-level analyses (Ferrer &

Widaman, 2008; Hamaker et al., 2005; Jones, 2007; Nesselroade & Ford, 1985;

Nesselroade & Molenaar, 1999; Velicer & Molenaar, 2013; West & Hepworth,

1991). Our work provides an additional procedure for using individual-level data

and making inferences about groups.

The common theme underlying our findings is the value of intraindividual

variability to describe individual processes (Nesselroade & Ford, 1985). In

particular, modeling such variability in a way that organizes both its structure

and its underlying dynamics is especially useful for capturing individual (or

dyadic) processes and their potential associations with distal outcomes. It is

up to the researcher to decide whether complex models such as the DAFS are

required to address theoretical questions of interest or if the standard deviation

of the time series, or other exploratory approaches (e.g., Ferrer et al., 2012),

are sufficient for the study of intraindividual variability. In either case, such

variability is informative about characteristics that would go untapped using

standard nomothetic methods.

ACKNOWLEDGMENTS

This research was supported in part by Grant BCS 052776 from the National

Science Foundation (Emilio Ferrer, PI). The first author thanks Keith Widaman

for suggesting the outline of this article. We acknowledge Dave Sbarra, Diane

Felmlee, Fushing Hsieh, and the members of the Dynamics of Dyadic Interac-

tions Project Lab at University of California, Davis. We also thank Stephen West

and three anonymous reviewers whose suggestions were invaluable for this work.

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