latent growth curve modeling in mplus: an introduction and practice examples part i

Latent Growth Curve Modeling In Mplus:Latent Growth Curve Modeling In Mplus:An Introduction and Practice ExamplesAn Introduction and Practice Examples

Part IPart I

Edward D. Barker, Ph.D.

Social, Genetic, and Developmental Psychiatry Centre Institute of Psychiatry, King’s College London

Acknowledgements

Bength & Linda Muthén Mplus: http://www.statmodel.com/

Alan A. Acock Department of HDFS

Oregon State University

Brigitte Wanner GRIP

University of Montréal

Outline

Introduction to Mplus Mplus & prog. language Preparing data Descriptive statistics

Basic growth Curve Model Basic Model and Assumption Mplus code Interpreting Output & Graphs

Quadratic terms Mplus program Interpreting Output & Graphs

Missing values in growth models Introduction Mplus code Output

Multiple group models At the same time As categorical predictors to

show differences in intercept and/or slope

Additional models There are many . . .

Introduction to Mplus

Input and output windows

Mplus Command Language (code, script, etc.)

Different commands divided into a series of sections TITLE

DATA (required)

VARIABLE (required)

DEFINE

ANALYSIS

MODEL

OUTPUT

SAVEDATA

MONTECARLO

Mplus Command Language (code, script, etc.)

TITLE: Everything after “Title:” is the title and the title ends when

“Data:” appears

DATA: Tells Mplus where to find the file containing the data.

“E:\Growth_Curves\ClassData.dat”

Without a specific path, Mplus will look in the same folder where the Mplus code is saved

Mplus Command Language (code, script, etc.)

VARIABLE: Series of subcommands that tell Mplus . . .

Names are names of variables (8 characters max; case sensitive in certain versions)

Missing are all (-99) ; tells Mplus user defined missing values

Use variables are names variables to use in the analysis. Useful if have larger data file for multiple purposes/analysis. IMPORTANT

ANALYSIS: Tells Mplus what type of analysis and estimator will be used

Type = basic ; (default)

Mplus Command Language (code, script, etc.)

MODEL: This contains the basic model statements

Y ON X ; ! regression

F1 BY var1@1 var2 var3 var4 ; ! Latent factors

var1 WITH var2 ; !correlation

OUTPUT: Lists specific statistical and graphical output wanted

Will get to this in the next section

Data and data preparation: SPSS to Mplus

Basic Analysis

Practice 1

Create Mplus data file from SPSS Write the translation file in SPSS

Check to make sure your data is correctly created

Conduct basic Mplus analysis Write the Mplus code

Outline

Introduction to Mplus Mplus & prog. language Preparing data Descriptive statistics

Basic growth Curve Model Basic Model and Assumption Mplus code Interpreting Output & Graphs

Quadratic terms Mplus program Interpreting Output & Graphs

Missing values in growth models Introduction Mplus code Output

Multiple group models At the same time As categorical predictors to

show differences in intercept and/or slope

Additional models There are many . . .

Basic Growth Curve Analysis

General latent variable framework Implemented in Mplus program Muthén and Muthén (1998-

2007)

Latent Growth Curve modeling / Structural Equation Modeling (SEM) is linked to Random Coefficient Growth Modeling / Multilevel modeling

Latent Growth Curve modeling (single population) is a “case“ of Growth Mixture Modeling (we cover this tomorrow)

Basic Growth Curve Analysis

Average growth within a population and its variation

Continuous latent variables (growth factors) capture individual differences in development Intercept (mean starting value)

Slope (rate of growth)

Quadratic term (leveling off, or coming down)

Basic Growth Curve Analysis

observed variables continuous censored binary ordinal count combinations

continuous latent variables measurement models (show an example later today)

Basic Growth Curve Analysis

Estimating a basic growth curve using Mplus is quite easy. In general, start simple, move to more complex

Basic Growth Curve Analysis

Intercept Slope

D12 D13 D14 D15 D16 D17

1.0 1.01.0

1.0 1.0 1.0

1.02.0 3.0 4.0

5.0

0.0

Mplus code for basic growth model

Selected growth curve output

Selected growth curve output

Selected growth curve output

Selected growth curve output

Selected growth curve output

Selected growth curve output

Selected growth curve output

Practice 2

Run basic growth curve model in Mplus Write Mplus code

Go through results and annotate the meaning of different parts of the results

Examine 2 graphs Individual observed values

Sample estimated means based on model

Outline

Introduction to Mplus Mplus & prog. language Preparing data Descriptive statistics

Basic growth Curve Model Basic Model and Assumption Mplus code Interpreting Output & Graphs

Quadratic terms Mplus program Interpreting Output & Graphs

Missing values in growth models Introduction Mplus code Output

Multiple group models At the same time As categorical predictors to

show differences in intercept and/or slope

Additional models There are many . . .

Growth Curve with a Quadratic Term

Intercept Slope

D12 D13 D14 D15 D16 D17

1.01.0 1.0

Quadratic

1.01.0

0.0 1.02.0 3.0 4.0

5.0

1.0

0.0

1.0 4.0 9.0

0.0

16.025.0

Mplus code for basic growth model with Quadratic Term

Selected output for quadratic model

Selected output for quadratic model

Selected output for quadratic model

Selected output for quadratic model

Practice 3

Run growth curve model with quradratic term Write Mplus code

Go through results and annotate the meaning of different parts of the results

Examine 2 graphs Estimated means based on model

Sample individual values

Outline

Introduction to Mplus Mplus & prog. language Preparing data Descriptive statistics

Basic growth Curve Model Basic Model and Assumption Mplus code Interpreting Output & Graphs

Quadratic terms Mplus program Interpreting Output & Graphs

Missing values in growth models Introduction Mplus code Output

Multiple group models At the same time As categorical predictors to

show differences in intercept and/or slope

Additional models There are many . . .

Missing values

Mplus has two ways of working with missing values full information maximum likelihood estimation with

missing values (FIML)

Multiple imputations.

1. Imputing multiple datasets

2. Estimating the model for each of these datasets

3. Then pooling the estimates and standard errors

Mplus code with missing data

Selected output for missing model

Selected output for missing model

Selected output for missing model

Selected output for missing model

Practice 4

Run growth curve model with missing analysis Write Mplus code

Go through results and annotate how the results change when using missing data analysis

Outline

Introduction to Mplus Mplus & prog. language Preparing data Descriptive statistics

Basic growth Curve Model Basic Model and Assumption Mplus code Interpreting Output & Graphs

Quadratic terms Mplus program Interpreting Output & Graphs

Missing values in growth models Introduction Mplus code Output

Multiple group models At the same time As categorical predictors to

show differences in intercept and/or slope

Additional models There are many . . .

Multiple group models

Gender Boys higher in delinquency

Several ways Compare models

Step 1: fit multiple model group and allow estimated parameters to vary

Step 2: constrain, at least intercept and slope

Multiple group models

Selected output: Multiple group models

Selected output: Multiple group models

Selected output: Multiple group models

Selected output: Multiple group models

Selected output: Multiple group models

Multiple group models: Constraints

Multiple group models: Constraints

Multiple group models: group as predictor

Group as predictor: Selected output

Practice 4

Practice A Run multiple groups with no restraints

Annotate output

Run multiple groups with restraints (intercept, slope) Annotate output

Practice B Add gender as predictor of intercept, slope, and

quadratic Annotate output

Other models

Here I am going to go through different models some of which you may end up using

Curran and Hussong (2003)

Conditional Linear Growth Curve: Covariate effectsConditional Linear Growth Curve: Covariate effects

Curran and Hussong (2003)

Parallel Conditional Linear Growth CurvesParallel Conditional Linear Growth Curves

Hancock, Kuo, and Lawrence (2001)

Second-order factors

First-order factors

Second-Order LGC ModelsSecond-Order LGC Models

Time-varying covariates

Combination of autoregressive cross-lagged model and LGCM

Difference scores (e.g., McArdle, 2001)

Two stage models (0-1; 1+) (see Mplus user’s guides)

ExtensionsExtensions

Maximum likelihood with robust standard errrors (MLR ) violate normal distribution

Satorra-Benter scaled chi-square difference test See Mplus for scaling correction factor http://www.statmodel.com/chidiff.shtml

Other estimatorsOther estimators

End Day 1

http://www2.chass.ncsu.edu/garson/pa765/statnote.htm

Change measured through random effects