Example of Confirmatory Factor Analysis with PROC CALIS

The script begins by creating a 'scores' dataset containing six numerical variables. Then, it uses the CALIS procedure three times with slight variations to illustrate different syntaxes and options. The first PROC CALIS block defines a simple factor model. The second block specifies paths more explicitly and customizes fit indices. The third block generates a path diagram to visualize the factor model. The latent factors 'verbal' and 'math' are linked respectively to variables 'x1-x3' and 'y1-y3'.

Data Analysis

Type : CREATION_INTERNE

The 'scores' dataset is created directly within the script via a DATA STEP block and the 'datalines' statement. It contains scores for 32 observations for 6 variables (x1-x3, y1-y3).

1 Code Block

DATA STEP Data

Explanation :
This DATA STEP block creates the 'scores' table by reading embedded data directly into the code using the 'datalines' statement. The table contains 6 numerical variables: x1, x2, x3, y1, y2, y3.

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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	;

2 Code Block

PROC CALIS

Explanation :
This block executes an initial confirmatory factor analysis. The 'factor' statement defines two latent factors: 'verbal' (linked to variables x1 to x3) and 'math' (linked to variables y1 to y3). The 'pvar' statement sets the variance of each factor to 1 for model identification.

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

3 Code Block

PROC CALIS

Explanation :
This second call to PROC CALIS shows an alternative syntax for the 'factor' statement, where each path between the factor and the variable is declared individually. The 'fitindex' option is used to select and display specific model fit indices (Chi-square, RMSEA, SRMR, etc.).

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1	title "Basic Confirmatory Factor Model: Separate Path Entries";
2	title2 "FACTOR Model Specification";
3	PROC CALIS DATA=scores;
4	factor
5	verbal ===> x1,
6	verbal ===> x2,
7	verbal ===> x3,
8	math ===> y1,
9	math ===> y2,
10	math ===> y3;
11	pvar
12	verbal = 1.,
13	math = 1.;
14	fitindex noindextype on(only)=[chisq df probchi rmsea srmr bentlercfi];
15	RUN;

4 Code Block

PROC CALIS

Explanation :
This third block activates ODS graphics via 'ods graphics on'. PROC CALIS is then called with the 'plots=pathdiagram' option to generate a visual representation of the factor model. The syntax '= 1.' in the 'factor' statement is another way to fix factor loadings for identification. Graphics are then deactivated with 'ods graphics off'.

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1	ods graphics on;
2	PROC CALIS DATA=scores plots=pathdiagram;
3	factor
4	verbal ===> x1-x3 = 1. ,
5	math ===> y1-y3 = 1. ;
6	RUN;
7	ods graphics off;

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