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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

An Example of Profiles from a Latent Class Analysis

Another Latent Class Analysis

Another Latent Class Analysis

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C1_.351 C2_.135 C3_.373 C4_.141

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%)

M Low Estimated

F Low Sample (57.8%)

F Low Estimated

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