Latent Growth Curve Modeling In Mplus:

1
Latent 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
2
Acknowledgements

• Bength Linda Muthén
• Mplus http//www.statmodel.com/
• Alan A. Acock
• Department of HDFS
• Oregon State University
• Brigitte Wanner
• GRIP
• University of Montréal

3
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 . . .

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Introduction to Mplus
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Input and output windows
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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

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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

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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)

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Mplus 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

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Data and data preparation SPSS to Mplus
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Basic Analysis
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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

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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 . . .

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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)

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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)

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Basic Growth Curve Analysis

• observed variables
• continuous
• censored
• binary
• ordinal
• count
• combinations
• continuous latent variables
• measurement models (show an example later today)

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Basic Growth Curve Analysis

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

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Basic 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
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Mplus code for basic growth model
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Selected growth curve output
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Selected growth curve output
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Selected growth curve output
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Selected growth curve output
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Selected growth curve output
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Selected growth curve output
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Selected growth curve output
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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

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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 . . .

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Growth 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
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Mplus code for basic growth model with Quadratic
Term
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Selected output for quadratic model
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Selected output for quadratic model
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Selected output for quadratic model
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Selected output for quadratic model
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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

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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 . . .

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Missing 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

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Mplus code with missing data
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Selected output for missing model
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Selected output for missing model
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Selected output for missing model
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Selected output for missing model
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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

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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 . . .

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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

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Multiple group models
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Selected output Multiple group models
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Selected output Multiple group models
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Selected output Multiple group models
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Selected output Multiple group models
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Selected output Multiple group models
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Multiple group models Constraints
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Multiple group models Constraints
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Multiple group models group as predictor
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Group as predictor Selected output
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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

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Other models

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

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Conditional Linear Growth Curve Covariate effects
Curran and Hussong (2003)
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Parallel Conditional Linear Growth Curves
Curran and Hussong (2003)
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Second-Order LGC Models
Second-order factors
First-order factors
Hancock, Kuo, and Lawrence (2001)
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Extensions

• 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)

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Other 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

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• End Day 1

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Change measured through random effects

• http//www2.chass.ncsu.edu/garson/pa765/statnote.h
  tm