Title: Latent Growth Curve Modeling In Mplus:
1Latent Growth Curve Modeling In Mplus An
Introduction and Practice Examples Part I
Edward D. Barker Ph.D.
Social Genetic and Developmental Psychiatry
Centre Institute of Psychiatry Kings
College London
2Acknowledgements
- Bength Linda Muthén
- Mplus http//www.statmodel.com/
- Alan A. Acock
- Department of HDFS
- Oregon State University
- Brigitte Wanner
- GRIP
- University of Montréal
3Outline
- 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 . . .
4Introduction to Mplus
5Input and output windows
6Mplus Command Language (code script etc.)
- Different commands divided into a series of
sections - TITLE
- DATA (required)
- VARIABLE (required)
- DEFINE
- ANALYSIS
- MODEL
- OUTPUT
- SAVEDATA
- MONTECARLO
7Mplus 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
8Mplus 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)
9Mplus Command Language (code script etc.)
- MODEL
- This contains the basic model statements
- Y ON X ! regression
- F1 BY var1_at_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
10Data and data preparation SPSS to Mplus
11Basic Analysis
12Practice 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
13Outline
- 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 . . .
14Basic 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)
15Basic 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)
16Basic Growth Curve Analysis
- observed variables
- continuous
- censored
- binary
- ordinal
- count
- combinations
- continuous latent variables
- measurement models (show an example later today)
17Basic Growth Curve Analysis
- Estimating a basic growth curve using Mplus is
quite easy. - In general start simple move to more complex
18Basic Growth Curve Analysis
Slope
Intercept
1.0
1.0
1.0
1.0
1.0
1.0
5.0
2.0
4.0
3.0
1.0
0.0
D12
D13
D14
D15
D16
D17
19Mplus code for basic growth model
20Selected growth curve output
21Selected growth curve output
22Selected growth curve output
23Selected growth curve output
24Selected growth curve output
25Selected growth curve output
26Selected growth curve output
27Practice 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
28Outline
- 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 . . .
29Growth Curve with a Quadratic Term
Slope
Quadratic
Intercept
0.0
4.0
9.0
1.0
16.0
25.0
1.0
0.0
1.0
1.0
1.0
1.0
1.0
5.0
2.0
4.0
3.0
1.0
0.0
D12
D13
D14
D15
D16
D17
30Mplus code for basic growth model with Quadratic
Term
31Selected output for quadratic model
32Selected output for quadratic model
33Selected output for quadratic model
34Selected output for quadratic model
35Practice 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
36Outline
- 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 . . .
37Missing values
- Mplus has two ways of working with missing values
- full information maximum likelihood estimation
with missing values (FIML) - Multiple imputations.
- Imputing multiple datasets
- Estimating the model for each of these datasets
- Then pooling the estimates and standard errors
38Mplus code with missing data
39Selected output for missing model
40Selected output for missing model
41Selected output for missing model
42Selected output for missing model
43Practice 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
44Outline
- 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 . . .
45Multiple 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
46Multiple group models
47Selected output Multiple group models
48Selected output Multiple group models
49Selected output Multiple group models
50Selected output Multiple group models
51Selected output Multiple group models
52Multiple group models Constraints
53Multiple group models Constraints
54Multiple group models group as predictor
55Group as predictor Selected output
56Practice 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
57Other models
- Here I am going to go through different models
some of which you may end up using
58Conditional Linear Growth Curve Covariate effects
Curran and Hussong (2003)
59Parallel Conditional Linear Growth Curves
Curran and Hussong (2003)
60Second-Order LGC Models
Second-order factors
First-order factors
Hancock Kuo and Lawrence (2001)
61Extensions
- 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 users
guides)
62Other estimators
- 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
63 64Change measured through random effects
- http//www2.chass.ncsu.edu/garson/pa765/statnote.h
tm
