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# Examine the evidence for measurement invariance of the five motivation items

INSTRUCTIONS TO CANDIDATES

Applied Longitudinal Data Analysis

For all questions, please type your answers. For coding questions, include the code and results that are directly relevant to your answers. Once finished, upload your completed assignment to Canvas and bring a copy to class on Monday. You may consult with your classmates when

working on this assignment but you must do all of the work yourself and write your own answers (words and code).

For the following two questions, use the mhs_edited datafile (downloadable on Canvas). The names of the variables are “id”, “pcomp_1”, “pcomp_2”, “pcomp_3”, “pcomp_4”, “motiv_1”, “motiv_2”, “motiv_3”, “motiv_4”, “mot1_1”, “mot2_1”, “mot3_1”, “mot4_1”, “mot5_1”, “mot1_4”, “mot2_4”, “mot3_4”, “mot4_4”, “mot5_4”. All numbers before the underscore refer to item number and all numbers after the underscore refer to the

assessment timepoint.

1. (3 points) Examine the evidence for measurement invariance of the five motivation items (i.e., mot1_1 – mot5_4) from the first wave (1) to the final wave (4). In particular, run four models – configural, weak, strong, and strict.

2. (1 point) Compare fit indices from the four measurement invariance models. Briefly describe (3-4 sentences) what you can conclude about the longitudinal factorial invariance of these items on the motivation scale.

For the following two questions, use the bivariate_4T.csv datafile (downloadable on Canvas). The names of the variables are "id", "read1", "read2", "read3", "read4", "math1", "math2", "math3", "math4". In these data, all of the assessments are equally spaced.

3. (2 points) Run separate univariate linear LGC models for read1– read4 and math1– math4. Then, run a bivariate LGC model including both reading and math scores.

4. (1 point) Interpret the level-level, level-slope, and slope-slope correlations from the previous question. Briefly describe (3-4 sentences) what these values represent.

For the following two questions, use the mhs_edited datafile.

5. (2 points) Run a cross-lagged panel model for the “pcomp” and “motiv” variables.

Note that these variables are composite scores of 4 and 5 items, respectively, across four timepoints. Correct for measurement unreliability by fixing the residual variances of “pcomp1-4” to be .08 and “motiv1-4” to be .07 (see slides 66-68 in Session_06_MV.pdf for justification). Additionally, constrain the autoregressive paths within each variable and the cross-lagged effects in the same direction to be equal.

6. (1 point) Interpret the autoregressive and cross-lagged effects from the previous question. Briefly describe what these values represent.

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