Example of Confirmatory Factor Analysis with PROC CALIS

The script begins by creating a 'scores' dataset containing six variables. Then, it performs three distinct analyses with PROC CALIS on this data. Each analysis tests a different measurement model for two latent factors ('verbal' and 'math'), imposing various constraints on factor loadings and error variances. This demonstrates the flexibility of the procedure for specifying structural equation models, ranging from a simple model with strong constraints to more complex models with freely estimated parameters.

Data Analysis

Type : CREATION_INTERNE

The 'scores' dataset is created directly in the script via a DATA step and the 'datalines' statement. There are no dependencies on external data.

1 Code Block

DATA STEP Data

Explanation :
This block creates the 'scores' table in memory (WORK library). Data is directly embedded in the code using the 'datalines' statement, which is common for examples or small datasets.

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1	DATA scores;
2	INPUT x1 x2 x3 y1 y2 y3;
3	DATALINES;
4	23 17 16 15 14 16
5	29 26 23 22 18 19
6	14 21 17 15 16 18
7	20 18 17 18 21 19
8	25 26 22 26 21 26
9	26 19 15 16 17 17
10	14 17 19 4 6 7
11	12 17 18 14 16 13
12	25 19 22 22 20 20
13	7 12 15 10 11 8
14	29 24 30 14 13 16
15	28 24 29 19 19 21
16	12 9 10 18 19 18
17	11 8 12 15 16 16
18	20 14 15 24 23 16
19	26 25 21 24 23 24
20	20 16 19 22 21 20
21	14 19 15 17 19 23
22	14 20 13 24 26 25
23	29 24 24 21 20 18
24	26 28 26 28 26 23
25	20 23 24 22 23 22
26	23 24 20 23 22 18
27	14 18 17 13 16 14
28	28 34 27 25 21 21
29	17 12 10 14 12 16
30	8 1 13 14 15 14
31	22 19 19 13 11 14
32	18 21 18 15 18 19
33	12 12 10 13 13 16
34	22 14 20 20 18 19
35	29 21 22 13 17 12
36	;
37

2 Code Block

PROC CALIS

Explanation :
This procedure performs a factor analysis on the 'scores' table. The 'FACTOR' statement defines a two-factor model ('verbal' and 'math'). The 'PVAR' statement imposes equality constraints: the three variables of the 'verbal' factor have the same error variance ('evar1'), and similarly for the 'math' factor ('evar2'). Factor variances are fixed to 1 for model identification.

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1	PROC CALIS DATA=scores;
2	factor
3	verbal ===> x1-x3 = load1 load1 load1,
4	math ===> y1-y3 = load2 load2 load2;
5	pvar
6	verbal = 1.,
7	math = 1.,
8	x1-x3 = 3*evar1,
9	y1-y3 = 3*evar2;
10	RUN;

3 Code Block

PROC CALIS

Explanation :
This second factor analysis is a variant of the first. The 'PVAR' statement is simplified to only fix the variance of the latent factors to 1. The error variances of the observed variables (x1-x3, y1-y3) are now freely estimated by the procedure, without equality constraints.

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1	PROC CALIS DATA=scores;
2	factor
3	verbal ===> x1-x3 = load1 load1 load1,
4	math ===> y1-y3 = load2 load2 load2;
5	pvar
6	verbal = 1.,
7	math = 1.;
8	RUN;

4 Code Block

PROC CALIS

Explanation :
This third analysis specifies a more complex model. In the 'FACTOR' statement, some factor loadings are freely estimated ('alpha', 'beta') while others are constrained. Similarly, in 'PVAR', some error variances are freely estimated ('phi', 'theta') and others are constrained to be equal. This shows how to specify models with partial constraints.

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1	PROC CALIS DATA=scores;
2	factor
3	verbal ===> x1-x3 = load1 load1 alpha,
4	math ===> y1-y3 = beta load2 load2;
5	pvar
6	verbal = 1.,
7	math = 1.,
8	x1-x3 = evar1 evar1 phi,
9	y1-y3 = theta evar2 evar2;
10	RUN;

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