I am doing a confirmatory factor analysis, using SEM, to construct three latent variables for subsequent use in a regression analysis.
I use the following command
Code:
sem (Visual -> v1, ) (Visual -> v2, ) (Visual -> v3, ) (Verbal -> v4, ) ///
(Verbal -> v5, ) (Verbal -> v6, ) (Speed -> v7, )(Speed -> v8, ) ///
(Speed -> v9, ), covstruct(_lexogenous, diagonal) vce(sbentler) ///
standardized latent(Visual Verbal Speed) ///
cov( Visual*Verbal Visual*Speed Verbal*Speed) nocapslatent
foreach v in Visual Verbal Speed {
predict `v', latent(`v')
egen std_`v'= std(`v') // standardized values
}
sum Visual Verbal Speed std_Visual std_Verbal std_Speed
PHP Code:
Endogenous variables
Measurement: v1 v2 v3 v4 v5 v6 v7 v8 v9
Exogenous variables
Latent: Visual Verbal Speed
Fitting target model:
Iteration 0: log pseudolikelihood = -4554.5345
Iteration 1: log pseudolikelihood = -4549.0267
Iteration 2: log pseudolikelihood = -4548.3346
Iteration 3: log pseudolikelihood = -4548.3322
Iteration 4: log pseudolikelihood = -4548.3322
Structural equation model Number of obs = 145
Estimation method = ml
Log pseudolikelihood = -4548.3322
( 1) [v1]Visual = 1
( 2) [v4]Verbal = 1
( 3) [v7]Speed = 1
-----------------------------------------------------------------------------------
| Satorra-Bentler
Standardized | Coef. Std. Err. z P>|z| [95% Conf. Interval]
------------------+----------------------------------------------------------------
Measurement |
v1 |
Visual | .67665 .0860549 7.86 0.000 .5079856 .8453145
_cons | 4.293115 .2497337 17.19 0.000 3.803646 4.782584
----------------+----------------------------------------------------------------
v2 |
Visual | .5165186 .0684681 7.54 0.000 .3823235 .6507137
_cons | 5.598598 .3782855 14.80 0.000 4.857172 6.340024
----------------+----------------------------------------------------------------
v3 |
Visual | .6935859 .069044 10.05 0.000 .5582622 .8289096
_cons | 1.926279 .0893687 21.55 0.000 1.75112 2.101439
----------------+----------------------------------------------------------------
v4 |
Verbal | .865565 .0332882 26.00 0.000 .8003213 .9308087
_cons | 2.958508 .1669357 17.72 0.000 2.63132 3.285696
----------------+----------------------------------------------------------------
v5 |
Verbal | .8293273 .0308301 26.90 0.000 .7689013 .8897533
_cons | 4.068081 .2698725 15.07 0.000 3.539141 4.597022
----------------+----------------------------------------------------------------
v6 |
Verbal | .8263318 .0355554 23.24 0.000 .7566445 .896019
_cons | 2.182157 .1137125 19.19 0.000 1.959285 2.405029
----------------+----------------------------------------------------------------
v7 |
Speed | .6591327 .0578271 11.40 0.000 .5457937 .7724717
_cons | 3.805027 .2013456 18.90 0.000 3.410397 4.199658
----------------+----------------------------------------------------------------
v8 |
Speed | .7958731 .0501476 15.87 0.000 .6975856 .8941605
_cons | 5.246285 .3948288 13.29 0.000 4.472435 6.020136
----------------+----------------------------------------------------------------
v9 |
Speed | .700846 .0517622 13.54 0.000 .5993938 .8022981
_cons | 5.196225 .3564262 14.58 0.000 4.497643 5.894808
------------------+----------------------------------------------------------------
var(e.v1)| .5421447 .1164581 .3558514 .8259653
var(e.v2)| .7332085 .0707301 .606897 .8858089
var(e.v3)| .5189386 .0957759 .3614243 .7451002
var(e.v4)| .2507973 .0576262 .1598602 .3934642
var(e.v5)| .3122162 .0511366 .2264857 .4303979
var(e.v6)| .3171758 .0587611 .220599 .4560333
var(e.v7)| .5655441 .0762315 .4342405 .7365506
var(e.v8)| .3665861 .0798222 .2392386 .5617211
var(e.v9)| .5088149 .0725547 .3847533 .6728796
var(Visual)| 1 . . .
var(Verbal)| 1 . . .
var(Speed)| 1 . . .
------------------+----------------------------------------------------------------
cov(Visual,Verbal)| .5406683 .0896913 6.03 0.000 .3648765 .7164601
cov(Visual,Speed)| .5233425 .0942191 5.55 0.000 .3386766 .7080085
cov(Verbal,Speed)| .3361288 .1131726 2.97 0.003 .1143146 .557943
-----------------------------------------------------------------------------------
LR test of model vs. saturated: chi2(24) = 51.54, Prob > chi2 = 0.0009
Satorra-Bentler scaled test: chi2(24) = 50.29, Prob > chi2 = 0.0013
.
. foreach v in Visual Verbal Speed {
2. predict `v', latent(`v')
3. egen std_`v'= std(`v') // standardized values
4. }
.
. sum Visual Verbal Speed std_Visual std_Verbal std_Speed
Variable | Obs Mean Std. Dev. Min Max
-------------+---------------------------------------------------------
Visual | 145 -4.32e-09 4.000018 -9.592437 12.42246
Verbal | 145 -1.23e-09 2.746986 -7.786823 7.084102
Speed | 145 3.21e-08 13.91826 -40.7785 43.87231
std_Visual | 145 2.20e-09 1 -2.398098 3.105601
std_Verbal | 145 -1.70e-10 1 -2.834679 2.578864
-------------+---------------------------------------------------------
std_Speed | 145 -1.02e-09 1 -2.929857 3.152141
1- Although I specified the standardized option, I still get the predicted variables with standard deviations more than 1, and I Why?
2- The mean of the predicted latent variables is always close to zero? If that is so, are we assuming the kappa; associated intercept in estimating the latent KSI, in the formula is equal to zero? Or in other words what kind of distribution for the latents Ksi in this model is assumed?
Bests,
Emma
0 Response to SEM and the predicted latent variable
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