Chapter 15, Multiple Indicator–Multiple Indicator Cause, Mixture, and Multilevel Models Video Solutions, A Beginner's Guide to Structural Equation Modeling

Problem 1

Create and run a LISREL-SIMPLIS program given the MIMIC model below. Please interpret the results including any model modification, significance of coefficients, and $\mathrm{R}^2$ value. The data set information is:
```
Observed Variables peer self income shift age
Sample Size 530
Correlation Matrix
1.00
```
The following MIMIC Model (next page) includes the latent variable job satisfaction (satisfac), which is defined in Figure 15.3 by two observed variables: peer ratings and self ratings. A person's income level, which shift they work, and age are observed predictor variables of job satisfaction.

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Problem 2

Given the following Miture Model in Figure 15.4 and data set information, write a LISREL program to test the Mixture Model. (Note: Robust
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statistics require the raw data file, so no Satorra-Bentler scaled chisquare possible). The Mixture Model has six observed variables (Age, Gender, Degree, Region, Hours, and Income) that define two latent variables (Person and Earning). A polyserial correlation matrix was created where CO indicates continuous variable and OR indicates a categorical variable. Age (CO), Gender (OR), and Degree (OR) define Personal characteristics, an independent latent variable (Person). Region (OR), Hours (CO), and Income (CO) define dependent latent variable Earning Power (Earning). Personal Characteristics (Person) is hypothesized to predict Earning Power (Earning).
The data for the Mixture Model is:
```
Observed Variables: Age Gender Degree Region Hours Income
Correlation Matrix
1.000
0.487 1.000
0.236 0.206 1.000
0.242 0.179 0.253 1.000
0.163 0.090 0.125 0.481 1.000
0.064 0.040 0.025 0.106 0.136 1.000
Means 15.00 10.000 10.000 10.000 7.000 10.000
Standard Deviations 10.615 10.000 8.000 10.000 15.701
10.000
Sample Size 600
```
The Mixture Model diagram is:
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Manik Pulyani

Numerade Educator

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Problem 3

You will need to access the directory, LISREL 8.8 Student Examples. Click on the mlevelex folder and select the PRELIS system file, income. $p s f$, which contains the variables region, state, age, gender, marital, etc. There are nine regions with 51 states nested within the regions. The sample size is $n=$ 6062. It is hypothesized that income varies by state within region.

Open the PRELIS system file, income.psf, and run three PRELIS multilevel model programs. The first model will be an intercept only model with income as the response variable, Level 3 or ID3 $=$ region, and Level 2 or ID2 $=$ state. The second PRELIS program will add gender as a fixed variable. The third PRELIS program will add an additional variable, marital, as a fixed variable. Use the multilevel pull-down menu on the tool bar to create the programs. (Note: Unselect the Intercept box in each dialog box).

List Model 1, Model 2, and Model 3 PRELIS programs and summarize the output from the three PRELIS programs in a table. You will need to hand calculate the intraclass correlation coefficient and be sure to interpret the comparative results in the table. The MODEL 1 dialog box should look like the following:
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Shu Naito

Numerade Educator