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1 2 3 4 5 6
+-------------------------------------------------+
1 | 1.032 |
2 | .473 .915 |
3 | .492 .528 1.017 |
4 | .269 .194 .235 1.062 |
5 | .18 .252 .249 .472 1.097 |
6 | .128 .18 .166 .38 .373 1.126 |
+-------------------------------------------------+
The code fragment starts off by defining a Mata function called myeval. The last line of myeval gives the discrepancy function which is being optimized (in this case minimized). Following the function definition the covariance matrix is entered as a regular Stata matrix. The program then goes into Mata to call the various optimize commands and options before ending with a series of output commands in Mata.p[ 1] - lambda-x[1,1] - variable 1 on factor 1 p[ 2] - lambda-x[2,1] - variable 2 on factor 1 p[ 3] - lambda-x[3,1] - variable 3 on factor 1 p[ 4] - lambda-x[4,2] - variable 4 on factor 2 p[ 5] - lambda-x[5,2] - variable 5 on factor 2 p[ 6] - lambda-x[6,2] - variable 6 on factor 2 p[ 7] - phi[2,1] - correlation between factors 1 and 2 p[ 8] - theta-delta[1,1] - unique factor variance for variable 1 p[ 9] - theta-delta[2,2] - unique factor variance for variable 2 p[10] - theta-delta[3,3] - unique factor variance for variable 3 p[11] - theta-delta[4,4] - unique factor variance for variable 4 p[12] - theta-delta[5,5] - unique factor variance for variable 5 p[13] - theta-delta[6,6] - unique factor variance for variable 6
mata: mata clear
mata:
void myeval(todo, p, s, lndetsn, fml, g, H)
{
l=J(6,2,0)
l[1..3,1]=p[1..3]'
l[4..6,2]=p[4..6]'
phi=I(2)
phi[2,1]=p[7]
phi[1,2]=p[7]
t=diag(p[8..13])
sigma = l*phi*l' + t
fml=log(det(sigma))+trace(invsym(sigma)*s)-lndetsn /* lndetsn = log(det(s))-n */
}
end
/* sample covariance matrix */
mat s = (1.032, ., ., ., ., . \ ///
.473, .915, ., ., ., . \ ///
.492, .528, 1.017, ., ., . \ ///
.269, .194, .235, 1.062, ., . \ ///
.180, .252, .249, .472, 1.097, . \ ///
.128, .180, .166, .380, .373, 1.126)
mata:
s=st_matrix("s")
_makesymmetric(s)
n=cols(s)
N=200
lndetsn=log(det(s))+n /* calculate once */
S=optimize_init()
optimize_init_which(S, "min")
optimize_init_evaluator(S, &myeval())
optimize_init_evaluatortype(S,"d0")
optimize_init_params(S, J(1,13,0.5))
optimize_init_argument(S, 1, s)
optimize_init_argument(S, 2, lndetsn)
p=optimize(S)
v=optimize_result_V(S)
v=diagonal(sqrt(diag(v)))'/sqrt(N/2)
mff=optimize_result_value(S)
/* output display */
p[1..3]',v[1..3]' /* lambda-x ksi 1 - se */
p[4..6]',v[4..6]' /* lambda-x ksi 2 - se */
p[7],v[7]' /* phi 2,1 - se */
p[8..13]\v[8..13] /* theta-delta / se */
1 :- (p[8..13] :/ diagonal(diag(s))') /* r-squared */
printf("Goodness of Fit Statistics \n")
df = n*(n+1)/2-cols(p)
chi2=N*mff
printf("degrees of freedom = %9.0f \n", df)
printf("chi-square = %9.4f \n", chi2)
printf("p-value = %9.4f \n", chi2tail(df,chi2))
printf("minimum fit function value = %9.4f \n", mff)
end
Iteration 0: f(p) = .39482661
Iteration 1: f(p) = .06234212 (not concave)
Iteration 2: f(p) = .04705071 (not concave)
Iteration 3: f(p) = .03954061 (not concave)
Iteration 4: f(p) = .03362923 (not concave)
Iteration 5: f(p) = .02607552 (not concave)
Iteration 6: f(p) = .02361655 (not concave)
Iteration 7: f(p) = .023476
Iteration 8: f(p) = .02265382
Iteration 9: f(p) = .02251722 (not concave)
Iteration 10: f(p) = .02246136
Iteration 11: f(p) = .02235127
Iteration 12: f(p) = .02234181
Iteration 13: f(p) = .02234179
/* lambda-x ksi 1 - se */
1 2
+-----------------------------+
1 | .6650460974 .0742902909 |
2 | .710899843 .0697524573 |
3 | .7417516958 .073515853 |
+-----------------------------+
/* lambda-x ksi 2 - se */
1 2
+-----------------------------+
1 | .691928814 .0887623678 |
2 | .6884025603 .0898251907 |
3 | .5401145259 .0874296577 |
+-----------------------------+
/* phi 2,1 - se */
1 2
+-----------------------------+
1 | .4606859412 .0867052696 |
+-----------------------------+
/* theta-delta / se */
1 2 3 4 5 6
+-------------------------------------------------------------------------------------+
1 | .5897136906 .4096214137 .4668044224 .5832345176 .623101863 .834276299 |
2 | .0779038385 .0694190998 .0768735571 .1030198761 .1050035395 .100803083 |
+-------------------------------------------------------------------------------------+
/* r-squared */
1 2 3 4 5 6
+-------------------------------------------------------------------------------------+
1 | .4285720052 .5523263239 .5409986014 .4508149552 .4319946554 .2590796634 |
+-------------------------------------------------------------------------------------+
Goodness of Fit Statistics
chi-square = 4.4684
p-value = 0.8126
minimum fit function value = 0.0223
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