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Structural Equation Modeling for Conducting Tests of Differences in Multiple Means

From the Division of Psychology in Education, Arizona State University, Tempe, Arizona.

View larger version (16K): [in a new window]   Figure 1. MANOVA using the SEM multiple-groups approach. Group 0 represents asthmatics with married parents, whereas group 1 represents asthmatics with recently divorced parents. V1 through V4 are the disengagement, denial, problem-focused coping, and seeking social support scales, respectively. The values on the paths between the estimated population mean () and the scales represent estimates of population means for the scales. For MI, the values are unconstrained and are estimates for the specific groups. For MC, these estimates are constrained to be equal between groups. For both MI and MC, the variances and covariances among the errors are assumed to be equal between groups.

View larger version (15K): [in a new window]   Figure 2. MANOVA using the SEM MIMIC approach. Vdummy is a 0-1 grouping variable with 0 being asthmatics with married parents and 1 being asthmatics with recently divorced parents. V1 through V4 are the disengagement, denial, problem-focused coping, and seeking social support scales, respectively. The values on the paths between the grouping variable and scales represent the estimated population effects of the grouping variable on the scales; that is, the estimated differences between scale means for asthmatics with married parents and asthmatics with recently divorced parents. For MI, these values are unconstrained and are estimated differences between the scale means for the adolescents with married parents and those with recently divorced parents. For MC, these estimates are constrained to 0.

View larger version (13K): [in a new window]   Figure 3. Discriminant analysis using the SEM MIMIC approach. Vduumy is a 0-1 grouping variable with 0 being asthmatics with married parents and 1 being asthmatics with recently divorced parents. V1 through V4 are the disengagement, denial, problem-focused coping, and seeking social support scales, respectively. For MI, the paths between the coping scales and F1 represent the weights applied to scales to form a linear combination that maximally differentiate the adolescents with married parents and those with recently divorced parents. For MC, the paths between the coping scales and the grouping variable (mediated by F1) are constrained to 0, not allowing the scales to differentiate groups.

View larger version (17K): [in a new window]   Figure 4. Assessment of differences in factor means using the SEM multiple-groups approach. Note: Groups 0 and 1 are asthmatics with married parents and asthmatics with recently divorced parents, respectively. V1 through V4 are the disengagement, denial, problem-focused coping, and seeking social support scales, respectively. F1 and F2 are the avoidant and active coping factors, respectively. The values on the paths between the estimated population mean () and the factors are the estimated population factor means. For both MI and MU, they are assigned a value of zero in group 0. For MI, the estimates for group 1 are unconstrained and allowed to differ from the estimates for group 0. For MC, the estimates for group 1 are constrained to be the same as the estimates for group 0 (i.e., 0). The values on the paths between the intercepts and the scales are the estimated population intercepts and are constrained to be equal across groups for both models.

View larger version (13K): [in a new window]   Figure 5. Assessment of differences in factor means using the SEM MIMIC model. Vduumy is a 0-1 grouping variable with 0 being asthmatics with married parents and 1 being asthmatics with recently divorced parents. V1 through V4 are the disengagement, denial, problem-focused coping, and seeking social support scales, respectively. F1 and F2 are the avoidant and active coping factors, respectively. The values on the paths between Vduumy and the factors represent the estimated population effects of Vduumy on the factors, that is, the estimated differences between factor means for asthmatics with married parents and those with recently divorced parents. These effects are unconstrained for MI (i.e., may differ from 0) and are constrained to zero for MC. The values on the paths between the factors and the scales represent the estimated population effects of the factors on the scales. The values for the first and third scales are constrained to 1 to define the metric of the factors.