Example 25 for PROC CALIS - Latent Growth Curve Model

The script starts by creating a 'growth' dataset via a DATA step with embedded data (datalines), representing repeated measures (y1 to y5). Then, it executes two distinct analyses with PROC CALIS. The first analysis fits a latent growth curve model with an equality constraint on error variances. The second analysis fits a similar model but without this constraint, allowing for the estimation of different error variances for each measurement time. The objective is to model growth using a latent intercept (f_alpha) and slope (f_beta).

Data Analysis

Type : CREATION_INTERNE

Data is generated and contained within the script itself using a DATA step and the 'datalines' statement, creating the 'growth' table.

1 Code Block

DATA STEP Data

Explanation :
This DATA STEP block creates the 'growth' table by reading 5 variables (y1 to y5) from data embedded directly in the code via the 'datalines' statement.

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1	DATA growth;
2	INPUT y1 y2 y3 y4 y5;
3	DATALINES;
4	17.6 21.4 25.6 32.1 37.7
5	13.2 14.3 18.9 20.3 25.4
6	11.6 13.5 17.4 22.1 39.6
7	10.7 11.1 13.2 18.2 21.4
8	18.7 23.7 28.6 31.5 34.0
9	18.3 19.2 20.5 23.2 25.9
10	9.2 13.5 17.8 19.2 21.1
11	18.3 23.5 27.9 30.2 34.6
12	11.2 15.6 20.8 22.7 30.4
13	17.0 22.9 26.9 31.9 35.6
14	10.4 13.6 18.0 25.6 29.3
15	17.7 19.0 22.5 28.5 30.7
16	14.5 19.4 21.1 28.8 31.5
17	20.0 21.4 28.9 30.2 35.6
18	14.6 19.3 21.7 28.5 32.0
19	11.7 15.2 19.1 23.7 28.7
20	;
21

2 Code Block

PROC CALIS

Explanation :
This block uses PROC CALIS to fit a latent growth curve model by maximum likelihood (method=ml). It defines linear equations (LINEQS) for observed variables as a function of a latent intercept (f_alpha) and slope (f_beta). A constraint is imposed so that the variances of the five error terms (e1-e5) are equal (5 * evar).

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1	PROC CALIS method=ml DATA=growth nostand noparmname;
2	lineqs
3	y1 = 0. * Intercept + f_alpha + e1,
4	y2 = 0. * Intercept + f_alpha + 1 * f_beta + e2,
5	y3 = 0. * Intercept + f_alpha + 2 * f_beta + e3,
6	y4 = 0. * Intercept + f_alpha + 3 * f_beta + e4,
7	y5 = 0. * Intercept + f_alpha + 4 * f_beta + e5;
8	variance
9	f_alpha f_beta,
10	e1-e5 = 5 * evar;
11	mean
12	f_alpha f_beta;
13	cov
14	f_alpha f_beta;
15	fitindex on(only)=[chisq df probchi];
16	RUN;

3 Code Block

PROC CALIS

Explanation :
This second PROC CALIS block fits a model similar to the previous one, but removes the constraint on error variances. The 'variance e1-e5;' statement allows for the estimation of a distinct variance for each error term, offering greater model flexibility.

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1	PROC CALIS method=ml DATA=growth nostand noparmname;
2	lineqs
3	y1 = 0. * Intercept + f_alpha + e1,
4	y2 = 0. * Intercept + f_alpha + 1 * f_beta + e2,
5	y3 = 0. * Intercept + f_alpha + 2 * f_beta + e3,
6	y4 = 0. * Intercept + f_alpha + 3 * f_beta + e4,
7	y5 = 0. * Intercept + f_alpha + 4 * f_beta + e5;
8	variance
9	f_alpha f_beta,
10	e1-e5;
11	mean
12	f_alpha f_beta;
13	cov
14	f_alpha f_beta;
15	fitindex on(only)=[chisq df probchi];
16	RUN;

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