PSY 9556B (Feb 12) Growth Mixture Modelingpublish.uwo.ca › ~ptrembla › longitudinal ›...
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PSY 9556B (Feb 12) Growth Mixture Modeling Let’s start with a brief introduction to other “clustering” techniques • Imagine a data file that you would to conduct an exploratory factor analysis (EFA) • The data has variables in columns and subjects in rows • The objective is to find a set of factors to explain the variables • It is possible to transpose the data file so that the variables are in rows and subjects in columns • You could now perform an EFA of subjects to determine if people fall into categories/prototypes/classes/types /clusters/profiles • This procedure is referred to as Q-technique (see Little, p. 227-228) • A somewhat similar procedure is cluster analysis • An alternative procedure is profile analysis using the multivariate approach to repeated measures (see chapter in Tabachnick and Fidell) • These techniques aim to identify meaningful groups of subjects similar on the variables of interest
Transcript of PSY 9556B (Feb 12) Growth Mixture Modelingpublish.uwo.ca › ~ptrembla › longitudinal ›...
PSY 9556B (Feb 12) Growth Mixture Modeling
Let’s start with a brief introduction to other “clustering” techniques • Imagine a data file that you would to conduct an exploratory factor analysis (EFA)
• The data has variables in columns and subjects in rows • The objective is to find a set of factors to explain the variables
• It is possible to transpose the data file so that the variables are in rows and subjects in columns
• You could now perform an EFA of subjects to determine if people fall into categories/prototypes/classes/types /clusters/profiles
• This procedure is referred to as Q-technique (see Little, p. 227-228) • A somewhat similar procedure is cluster analysis • An alternative procedure is profile analysis using the multivariate approach to
repeated measures (see chapter in Tabachnick and Fidell) • These techniques aim to identify meaningful groups of subjects similar on the
variables of interest
An Example of Profiles from a Latent Class Analysis
Another Latent Class Analysis
Another Latent Class Analysis
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Figure 4. Classes obtained from Latent class analysis. Proportions indicated in legend above. Responses refer to “problems with your emotions, mental health, use of alcohol or drugs, or experiences of violence?” These classes could be labeled as (1) No Use of Services (2) Psychiatrist/Doctor/Friend/Family/Social Worker (3) Friend/Family (4) Friend/Family/Doctor/Coworker/Nurse.
Alternative Way of Plotting Results
Figure 4. Classes obtained from Latent class analysis. Proportions indicated in legend above. Responses refer to “problems with your emotions, mental health, use of alcohol or drugs, or experiences of violence?” These classes could be labeled as (1) No Use of Services (2) Psychiatrist/Doctor/Friend/Family/Social Worker (3) Friend/Family (4) Friend/Family/Doctor/Coworker/Nurse.
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Psychiat Doctor Psychol Nurse SocWk Family Friend Cowork Minister Teach Police
Class1_35% Class2_13.5% Class3_37.3% Class4_14.1%
Latent Class Analysis
• LCA uses a modelling approach to derive the classes (categorical items) • Latent profile analysis (continuous items) • A specific number of classes tested in steps
• Start with one class and see if model improves in fit by adding a second class
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y/u2 y/u3 y/u4 y/u1
Unordered latent class variable with K categories Item parameters are
probabilities for categorical items and means/variances for continuous items
threshold to probability
LCA – Deciding on Number of Classes (applies also to GMM)
• The number of classes to model is determined by comparing models differing in number of classes
• The chi-square difference test based on the likelihood ratio not appropriate for LCA
• An approximation by Lo, Mendell, and Rubin (2001) has been proposed • Mplus program provides bootstrap likelihood ratio test (BLTR) as a test to
compare the increase in model fit by adding a class. • Can also use Akaike’s Information Criterion (AIC; Akaike, 1987) and the
Bayesian Information Criterion (BIC; Schwartz, 1978) • Entropy, indicates the precision of classification (Magidson & Vermunt,
2002) • Theory • Number of individual in classes
LCA – Reporting Analyses for Selection of Number of Classes
See figure, slide 2
EFA vs. LCA Example
EFA vs. LCA Example
EFA vs. LCA Example
Growth Mixture Modeling
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M High Sample (2.0%)
M High Estimated
M Low Sample (33.7%)
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F Low Sample (57.8%)
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F High Sample (6.5%)
F High Estimated
VARIABLE: NAMES ARE dep1-dep8; CLASSES = cg (2) c (2); KNOWNCLASSES = cg (g = 0 g = 1);
Growth Mixture Modeling
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Group1 Sample (9.2%)
Group1 Estimated
Group2 Sample (5.0%)
Group2 Estimated
Group3 Sample (85.7%)
Group3 Estimated
Growth Mixture Modeling 1 2 3 4 5 6 7 8
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Growth Mixture Modeling: Another Example Start with a LGM Model
LGM Output
GMM 2 Classes
GMM Two Classes
GMM 2 Classes
GMM 2 Classes
GMM 2 Classes
GMM 3 Classes
GMM 3 Classes
GMM 3 Classes
GMM 3 Classes
GMM 4 Classes
