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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, King’s College London. Bength & Linda Muth é n Mplus: http://www.statmodel.com/ Alan A. Acock - PowerPoint PPT Presentation
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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