Documentation Example 26 for PROC CALIS
/****************************************************************/
/* S A S S A M P L E L I B R A R Y */
/* */
/* NAME: CALEX08 */
/* TITLE: Documentation Example 26 for PROC CALIS */
/* PRODUCT: STAT */
/* SYSTEM: ALL */
/* KEYS: higher-order and hierarchical factor models */
/* PROCS: CALIS */
/* DATA: */
/* */
/* SUPPORT: yiyung UPDATE: August 27, 2007 */
/* REF: PROC CALIS, Example 26 */
/* MISC: */
/****************************************************************/
data Thurst(type=corr);
title "Example of THURSTONE resp. McDONALD (1985, p.57, p.105)";
_type_ = 'corr'; input _name_ $ V1-V9;
label V1='Sentences' V2='Vocabulary' V3='Sentence Completion'
V4='First Letters' V5='Four-letter Words' V6='Suffices'
V7='Letter series' V8='Pedigrees' V9='Letter Grouping';
datalines;
V1 1. . . . . . . . .
V2 .828 1. . . . . . . .
V3 .776 .779 1. . . . . . .
V4 .439 .493 .460 1. . . . . .
V5 .432 .464 .425 .674 1. . . . .
V6 .447 .489 .443 .590 .541 1. . . .
V7 .447 .432 .401 .381 .402 .288 1. . .
V8 .541 .537 .534 .350 .367 .320 .555 1. .
V9 .380 .358 .359 .424 .446 .325 .598 .452 1.
;
proc calis corr data=Thurst method=max nobs=213 nose nostand;
lineqs
V1 = X11 * Factor1 + E1,
V2 = X21 * Factor1 + E2,
V3 = X31 * Factor1 + E3,
V4 = X42 * Factor2 + E4,
V5 = X52 * Factor2 + E5,
V6 = X62 * Factor2 + E6,
V7 = X73 * Factor3 + E7,
V8 = X83 * Factor3 + E8,
V9 = X93 * Factor3 + E9,
Factor1 = L1g * FactorG + E10,
Factor2 = L2g * FactorG + E11,
Factor3 = L3g * FactorG + E12;
variance
FactorG = 1. ,
E1-E12 = U1-U9 W1-W3;
bounds
0. <= U1-U9;
fitindex ON(ONLY)=[chisq df probchi];
/* SAS Programming Statements: Dependent parameter definitions */
W1 = 1. - L1g * L1g;
W2 = 1. - L2g * L2g;
W3 = 1. - L3g * L3g;
run;
proc calis corr data=Thurst method=max nobs=213 nose nostand;
lineqs
V1 = X11 * Factor1 + X1g * FactorG + E1,
V2 = X21 * Factor1 + X2g * FactorG + E2,
V3 = X31 * Factor1 + X3g * FactorG + E3,
V4 = X42 * Factor2 + X4g * FactorG + E4,
V5 = X52 * Factor2 + X5g * FactorG + E5,
V6 = X62 * Factor2 + X6g * FactorG + E6,
V7 = X73 * Factor3 + X7g * FactorG + E7,
V8 = X83 * Factor3 + X8g * FactorG + E8,
V9 = X93 * Factor3 + X9g * FactorG + E9;
variance
Factor1-Factor3 = 3 * 1.,
FactorG = 1. ,
E1-E9 = U1-U9;
cov
Factor1-Factor3 FactorG = 6 * 0.;
bounds
0. <= U1-U9;
fitindex ON(ONLY)=[chisq df probchi];
run;
data _null_;
df0 = 24; chi0 = 38.1963;
df1 = 18; chi1 = 24.2163;
diff = chi0-chi1;
p = 1.-probchi(chi0-chi1,df0-df1);
put 'Chi-square difference = ' diff;
put 'p-value = ' p;
run;
proc calis corr data=Thurst method=max nobs=213 nose nostand;
lineqs
V1 = X11 * Factor1 + X1g * FactorG + E1,
V2 = X21 * Factor1 + X2g * FactorG + E2,
V3 = X31 * Factor1 + X3g * FactorG + E3,
V4 = X42 * Factor2 + X4g * FactorG + E4,
V5 = X52 * Factor2 + X5g * FactorG + E5,
V6 = X62 * Factor2 + X6g * FactorG + E6,
V7 = X73 * Factor3 + X7g * FactorG + E7,
V8 = X83 * Factor3 + X8g * FactorG + E8,
V9 = X93 * Factor3 + X9g * FactorG + E9;
variance
Factor1-Factor3 = 3 * 1.,
FactorG = 1. ,
E1-E9 = U1-U9;
cov
Factor1-Factor3 FactorG = 6 * 0.;
bounds
0. <= U1-U9;
fitindex ON(ONLY)=[chisq df probchi];
parameters p1 (.5) p2 (.5) p3 (.5);
/* Proportionality constraints */
X1g = p1 * X11;
X2g = p1 * X21;
X3g = p1 * X31;
X4g = p2 * X42;
X5g = p2 * X52;
X6g = p2 * X62;
X7g = p3 * X73;
X8g = p3 * X83;
X9g = p3 * X93;
run;