Transcript Document

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
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
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


Mplus & prog. language
Preparing data
Descriptive statistics
Basic Model and Assumption
Mplus code
Interpreting Output & Graphs
Missing values in growth
models
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

Basic growth Curve Model
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Multiple group models
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Quadratic terms
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Mplus program
Interpreting Output & Graphs

Introduction
Mplus code
Output
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 Model and Assumption
Mplus code
Interpreting Output & Graphs
Missing values in growth
models



Basic growth Curve Model






Multiple group models


Quadratic terms


Mplus program
Interpreting Output & Graphs

Introduction
Mplus code
Output
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 (19982007)
 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
Slope
Intercept
1.0
1.0
0.0
D12
1.0
1.0
1.0
D13
2.0
D14
1.0
1.0
3.0
D15
5.0
4.0
D16
D17
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 Model and Assumption
Mplus code
Interpreting Output & Graphs
Missing values in growth
models



Basic growth Curve Model






Multiple group models


Quadratic terms


Mplus program
Interpreting Output & Graphs

Introduction
Mplus code
Output
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
Slope
Intercept
Quadratic
0.0
1.0
1.0
1.0
0.0
D12
1.0
1.0
1.0
D13
2.0
D14
4.0
9.0
1.0
1.0
3.0
D15
16.0
25.0
0.0
5.0
4.0
D16
D17
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 Model and Assumption
Mplus code
Interpreting Output & Graphs
Missing values in growth
models



Basic growth Curve Model






Multiple group models


Quadratic terms


Mplus program
Interpreting Output & Graphs

Introduction
Mplus code
Output
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 Model and Assumption
Mplus code
Interpreting Output & Graphs
Missing values in growth
models



Basic growth Curve Model






Multiple group models


Quadratic terms


Mplus program
Interpreting Output & Graphs

Introduction
Mplus code
Output
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
Conditional Linear Growth Curve: Covariate effects
Curran and Hussong (2003)
Parallel Conditional Linear Growth Curves
Curran and Hussong (2003)
Second-Order LGC Models
Second-order
factors
First-order
factors
Hancock, Kuo, and Lawrence (2001)
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 user’s guides)
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
End Day 1
Change measured through random effects

http://www2.chass.ncsu.edu/garson/pa765/statnote
.htm