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
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 . . .
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