Table 8.1 on page 282.
Part 1: Excerpt from the multivariate format data set.
data alcohol2; set alda.alcohol2; alc1 = exp(alc1); alc2 = exp(alc2); alc3 = exp(alc3); peer1 = exp(peer1); peer2 = exp(peer2); peer3 = exp(peer3); if id in (18, 21, 236, 335, 353, 555, 850, 883, 974, 1012); run; proc print data = alcohol2 noobs; format alc1-alc3 4.2 peer1-peer3 female 3.0; run;
ID FEMALE ALC1 ALC2 ALC3 PEER1 PEER2 PEER3
18 0 1.00 1.33 2.00 3 2 2 21 0 2.00 1.00 1.33 1 5 5 236 0 3.33 4.33 4.33 2 1 4 335 0 1.00 1.33 1.67 1 2 1 353 0 2.00 2.00 1.67 1 1 2 555 1 2.67 2.33 1.67 2 3 1 850 1 1.33 1.67 1.33 3 1 2 883 1 3.00 2.67 3.33 4 5 1 974 1 1.00 1.67 2.67 1 5 6 1012 1 1.00 1.67 2.33 1 2 4
Part 2: Estimated means and variance/covariance matrix for transformed data.
proc means data = alda.alcohol2 mean; var female alc1-alc3 peer1-peer3; run;
The MEANS Procedure
Variable Mean ------------------------ FEMALE 0.6122995 ALC1 0.2250666 ALC2 0.2541351 ALC3 0.2879230 PEER1 0.1771944 PEER2 0.2904569 PEER3 0.3470381 ------------------------
proc corr data = alda.alcohol2 ; var female alc1-alc3 peer1-peer3; ods output cov = cov ; run; proc print data = cov noobs; format _numeric_ 5.3; run;
Variable FEMALE ALC1 ALC2 ALC3 PEER1 PEER2 PEER3
FEMALE 0.238 -.008 -.013 -.005 -.009 -.022 -.024 ALC1 -.008 0.136 0.078 0.065 0.066 0.064 0.060 ALC2 -.013 0.078 0.155 0.082 0.045 0.096 0.074 ALC3 -.005 0.065 0.082 0.181 0.040 0.066 0.132 PEER1 -.009 0.066 0.045 0.040 0.174 0.072 0.071 PEER2 -.022 0.064 0.096 0.066 0.072 0.262 0.112 PEER3 -.024 0.060 0.074 0.132 0.071 0.112 0.289
Table 8.2 on page 289.
Model A:
data al2;
set alda.alcohol2;
cons = 1;
run;
/*model A*/
proc calis noint ucov data = al2 method=ml;
lineqs
alc1 = F1 + 0 F2 + E1,
alc2 = F1 + .75 F2 + E2,
alc3 = F1 + 1.75 F2 + E3,
f1 = b1 cons + d1,
f2 = b2 cons + d2;
std
d1-d2 = 2 * A: (2 * 3.) ,
e1-e3 = 3* A: (3 *3.);
cov
d2 d1 = cov;
run;
quit;
The CALIS Procedure Covariance Structure Analysis: Maximum Likelihood Estimation
Chi-Square 0.0482 Chi-Square DF 1 Pr > Chi-Square 0.8263
Latent Variable Equations with Estimates
f1 = 0.2256*cons + 1.0000 d1 Std Err 0.0107 b1 t Value 21.0970 f2 = 0.0360*cons + 1.0000 d2 Std Err 0.00735 b2 t Value 4.8958
Variances of Exogenous Variables
Standard Variable Parameter Estimate Error t Value
cons 1.00089 E1 A3 0.04847 0.00642 7.55 E2 A4 0.07577 0.00445 17.04 E3 A5 0.07677 0.00990 7.75 d1 A1 0.08712 0.00711 12.25 d2 A2 0.01978 0.00522 3.79
Covariances Among Exogenous Variables
Standard Var1 Var2 Parameter Estimate Error t Value
d1 d2 cov -0.01249 0.00458 -2.73
Model B:
proc calis noint ucov data = al2 method=ml;
lineqs
alc1 = F1 + 0 F2 + E1,
alc2 = F1 + .75 F2 + E2,
alc3 = F1 + 1.75 F2 + E3,
f1 = b1 cons + c1 female + d1,
f2 = b2 cons + c2 female + d2;
std
d1-d2 = 2 * A: (2 * 3.) ,
e1-e3 = 3 * A: (3 *3.);
cov
d2 d1 = cov;
run;
quit;
The CALIS Procedure Covariance Structure Analysis: Maximum Likelihood Estimation Chi-Square 1.5434 Chi-Square DF 2 Pr > Chi-Square 0.4622
Latent Variable Equations with Estimates
f1 = -0.0419*FEMALE + 0.2513*cons + 1.0000 d1 Std Err 0.0219 c1 0.0171 b1 t Value -1.9128 14.6546 f2 = 0.00788*FEMALE + 0.0312*cons + 1.0000 d2 Std Err 0.0151 c2 0.0118 b2 t Value 0.5222 2.6401
Variances of Exogenous Variables
Standard Variable Parameter Estimate Error t Value
FEMALE 0.61285 cons 1.00089 E1 A3 0.04890 0.00642 7.62 E2 A4 0.07556 0.00444 17.03 E3 A5 0.07715 0.00990 7.79 d1 A1 0.08640 0.00709 12.19 d2 A2 0.01950 0.00521 3.74
Covariances Among Exogenous Variables
Standard Var1 Var2 Parameter Estimate Error t Value
FEMALE cons 0.61285 d1 d2 cov -0.01217 0.00457 -2.66
Baseline model to be compared with for model B:
proc calis noint ucov data = al2 method=ml;
lineqs
alc1 = F1 + 0 F2 + E1,
alc2 = F1 + .75 F2 + E2,
alc3 = F1 + 1.75 F2 + E3,
f1 = b1 cons + 0 female + d1,
f2 = b2 cons + 0 female + d2;
std
d1-d2 = 2 * A: (2 * 3.) ,
e1-e3 = 3 * A: (3 *3.);
cov
d2 d1 = cov;
run;
quit;
The CALIS Procedure Covariance Structure Analysis: Maximum Likelihood Estimation
Chi-Square 5.3617 Chi-Square DF 4 Pr > Chi-Square 0.2522
Model C:
proc calis noint ucov data = al2 method=ml;
lineqs
alc1 = F1 + 0 F2 + E1,
alc2 = F1 + .75 F2 + E2,
alc3 = F1 + 1.75 F2 + E3,
f1 = b1 cons + b3 female + d1,
f2 = b2 cons + 0 female + d2;
std
d1-d2 = 2 * A: (2 * 3.) ,
e1-e3 = 3 * A: (3 *3.);
cov
d2 d1 = cov;
run;
quit;
The CALIS Procedure Covariance Structure Analysis: Maximum Likelihood Estimation Chi-Square 1.8157 Chi-Square DF 3 Pr > Chi-Square 0.6115
Latent Variable Equations with Estimates
f1 = -0.0366*FEMALE + 0.2480*cons + 1.0000 d1 Std Err 0.0194 b3 0.0160 b1 t Value -1.8861 15.5264 f2 = 0.0360*cons + 1.0000 d2 Std Err 0.00735 b2 t Value 4.8958
Variances of Exogenous Variables
Standard Variable Parameter Estimate Error t Value
FEMALE 0.61285 cons 1.00089 E1 A3 0.04884 0.00642 7.61 E2 A4 0.07556 0.00444 17.03 E3 A5 0.07726 0.00990 7.80 d1 A1 0.08645 0.00709 12.19 d2 A2 0.01950 0.00521 3.74
Covariances Among Exogenous Variables
Standard Var1 Var2 Parameter Estimate Error t Value
FEMALE cons 0.61285 d1 d2 cov -0.01220 0.00457 -2.67
Model D:
proc calis noint ucov data = al2 method=ml;
lineqs
alc1 = F1 + 0 F2 + E1,
alc2 = F1 + .75 F2 + E2,
alc3 = F1 + 1.75 F2 + E3,
peer1 = f11 + 0 f22 + e4,
peer2 = f11 + .75 f22 + e5,
peer3 = f11 + 1.75 f22 + e6,
f1 = b1 cons + c11 f11 + c12 f22 + d3,
f2 = b2 cons + c21 f11 + c22 f22 + d4,
f11 = b3 cons + d1,
f22 = b4 cons + d2;
std
d1-d4 = 4 * A: (4 * 3.),
e1-e6 = 6 * A: (6 *3.) ;
cov
d1 d2 = cov0, /* covariance of pi_0' and pi_1' */
d3 d4 = cov1, /* covariance of pi_0 and pi_1*/
e1 e4 = cov3, /* covariance of delta1 and epsilon1 */
e2 e5 = cov4, /* covarinace of delta2 and epsilon2 */
e3 e6 = cov5; /* covarinace of delta3 and epsilon3 */
run;
quit;
The CALIS Procedure Covariance Structure Analysis: Maximum Likelihood Estimation
Chi-Square 11.5469 Chi-Square DF 4 Pr > Chi-Square 0.0211
Latent Variable Equations with Estimates
f1 = 0.7986*f11 + 0.0804*f22 + 0.0666*cons + 1.0000 d3 Std Err 0.1023 c11 0.1824 c12 0.0156 b1 t Value 7.8072 0.4410 4.2699
f2 = -0.1433*f11 + 0.5767*f22 + 0.00830*cons + 1.0000 d4 Std Err 0.0759 c21 0.1922 c22 0.0145 b2 t Value -1.8876 3.0008 0.5715
f11 = 0.1882*cons + 1.0000 d1 Std Err 0.0119 b3 t Value 15.7882
f22 = 0.0962*cons + 1.0000 d2 Std Err 0.00966 b4 t Value 9.9512
Variances of Exogenous Variables
Standard Variable Parameter Estimate Error t Value
cons 1.00089 E1 A5 0.04808 0.00636 7.56 E2 A6 0.07628 0.00443 17.23 E3 A7 0.07635 0.00975 7.83 e4 A8 0.10588 0.01075 9.85 e5 A9 0.17143 0.00873 19.65 e6 A10 0.12907 0.01756 7.35 d3 A3 0.04220 0.00745 5.67 d4 A4 0.00923 0.00542 1.70 d1 A1 0.06975 0.01036 6.73 d2 A2 0.02850 0.00884 3.22
Covariances Among Exogenous Variables
Standard Var1 Var2 Parameter Estimate Error t Value
E1 e4 cov3 0.01094 0.00613 1.78 E2 e5 cov4 0.03403 0.00466 7.31 E3 e6 cov5 0.03745 0.01019 3.68 d3 d4 cov1 -0.00637 0.00509 -1.25 d1 d2 cov0 0.00118 0.00707 0.17
Baseline model for comparing with model D:
proc calis noint ucov data = al2 method=ml;
lineqs
alc1 = F1 + 0 F2 + E1,
alc2 = F1 + .75 F2 + E2,
alc3 = F1 + 1.75 F2 + E3,
peer1 = f11 + 0 f22 + e4,
peer2 = f11 + .75 f22 + e5,
peer3 = f11 + 1.75 f22 + e6,
f1 = b1 cons + 0 f11 + 0 f22 + d3,
f2 = b2 cons + 0 f11 + 0 f22 + d4,
f11 = b3 cons + d1,
f22 = b4 cons + d2;
std
d1-d4 = 4 * A: (4 * 3.),
e1-e6 = 6 * A: (6 *3.) ;
cov
d1 d2 = cov0, /* covariance of pi_0' and pi_1' */
d3 d4 = cov1, /* covariance of pi_0 and pi_1*/
e1 e4 = cov3, /* covariance of delta1 and epsilon1 */
e2 e5 = cov4, /* covarinace of delta2 and epsilon2 */
e3 e6 = cov5; /* covarinace of delta3 and epsilon3 */
run;
quit;
The CALIS Procedure Covariance Structure Analysis: Maximum Likelihood Estimation
Chi-Square 342.3423 Chi-Square DF 8 Pr > Chi-Square <.0001