help: lmnsem dialog:

Title

lmnsem: Overall System Non Normality Tests after (SEM) Regressions

Syntax

lmnsem

Description

lmnsem computes overall system Non Normality Tests, after:

- (SEM) Structural Equation Modeling Regressions sem for system of simultaneous equations.

Saved Results

lmnsem saves the following in r():

Scalars

r(lmnjb_#) Jarque-Bera LM Test for eq.#
r(lmnjbp_#) Jarque-Bera LM Test for eq.# P-Value

r(lmnjb) Jarque-Bera LM Test
r(lmnjbp) Jarque-Bera LM Test P-Value
r(lmndh) Doornik-Hansen LM Test
r(lmndhp) Doornik-Hansen LM Test P-Value
r(lmng) Geary LM Test
r(lmngp) Geary LM Test P-Value
r(lmnad) Anderson-Darling Z Test
r(lmnadp) Anderson-Darling Z Test P-Value
r(lmndp) D'Agostino-Pearson LM Test
r(lmndpp) D'Agostino-Pearson LM Test P-Value
r(lmnsvs) Srivastava LM Skewness Test
r(lmnsvsp) Srivastava LM Skewness Test P-Value
r(lmnsms1) Small LM Skewness Test
r(lmnsms1p) Small LM Skewness Test P-Value
r(lmnsms2) Skewness Z Test
r(lmnsms2p) Skewness Z Test P-Value
r(lmnsvk) Srivastava Z Kurtosis Test
r(lmnsvkp) Srivastava Z Kurtosis Test P-Value
r(lmnsmk1) Small LM Kurtosis Test
r(lmnsmk1p) Small LM Kurtosis Test P-Value
r(lmnsmk2) Kurtosis Z Test
r(lmnsmk2p) Kurtosis Z Test P-Value
r(sk) Skewness Coefficient
r(sksd) Skewness Standard Deviation
r(ku) Kurtosis Coefficient
r(kusd) Kurtosis Standard Deviation
r(sn) Standard Deviation Runs Sig(k)
r(en) Mean Runs E(k)
r(lower) Lower 95% Conf. Interval [E(k)- 1.96* Sig(k)]
r(upper) Upper 95% Conf. Interval [E(k)+ 1.96* Sig(k)]

References

Anderson T.W., Darling D.A. (1954)
"A Test of Goodness of Fit",
Journal of the American Statisical Association, 49; 765–69.

C.M. Jarque & A.K. Bera (1987)
"A Test for Normality of Observations and Regression Residuals"
International Statistical Review , Vol. 55; 163-172.

D'Agostino, R. B., & Rosman, B. (1974)
"The Power of Geary’s Test of Normality",
Biometrika, 61(1); 181-184.

Damodar Gujarati (1995)
"Basic Econometrics"
3rd Edition, McGraw Hill, New York, USA.

Geary R.C. (1947)
"Testing for Normality" Biometrika, Vol. 34; 209-242.

Geary R.C. (1970)
"Relative Efficiency of Count of Sign Changes for Assessing Residuals Autoregression in Least Squares Regression"
Biometrika, Vol. 57; 123-127.

Pearson, E. S., D'Agostino, R. B., & Bowman, K. O. (1977)
"Tests for Departure from Normality: Comparison of Powers",
Biometrika, 64(2); 231-246.

Examples

in this example FIML will be used as follows:

clear all

sysuse lmnsem.dta , clear

sem (y1 <- y2 x1 x2) (y2 <- y1 x3 x4), cov(e.y1*e.y2)

lmnsem

return list

* If you want to use dialog box: Press OK to compute lmnsem

db lmnsem

. clear all
. sysuse lmnsem.dta , clear
. sem (y1 <- y2 x1 x2) (y2 <- y1 x3 x4), cov(e.y1*e.y2)

Structural equation model Number of obs = 17
Estimation method = ml
Log likelihood = -363.34588
------------------------------------------------------------------------------
| OIM
| Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
Structural |
y1 <- |
y2 | .2425937 .2106232 1.15 0.249 -.1702201 .6554075
x1 | .2568409 .462485 0.56 0.579 -.649613 1.163295
x2 | -1.037016 .3154059 -3.29 0.001 -1.6552 -.4188317
_cons | 147.0826 54.4491 2.70 0.007 40.36431 253.8009
-----------+----------------------------------------------------------------
y2 <- |
y1 | -.6282929 .6148239 -1.02 0.307 -1.833326 .5767398
x3 | -.5226661 .3235637 -1.62 0.106 -1.156839 .1115071
x4 | 3.4208 1.440664 2.37 0.018 .5971513 6.244449
_cons | 62.44495 42.36071 1.47 0.140 -20.58052 145.4704
-------------+----------------------------------------------------------------
Variance |
e.y1 | 80.17577 28.99122 39.46865 162.8673
e.y2 | 142.4478 80.80501 46.86006 433.0208
-------------+----------------------------------------------------------------
Covariance |
e.y1 |
e.y2 | 25.62619 53.75243 0.48 0.634 -79.72665 130.979
------------------------------------------------------------------------------
LR test of model vs. saturated: chi2(2) = 0.12, Prob > chi2 = 0.9408

. lmnsem

=================================================
* System Non Normality Tests (ml)
=================================================
*** Single Equation Non Normality Tests:
Ho: Normality - Ha: Non Normality

Eq. 1 : Jarque-Bera LM Test = 2.6232 P-Value > Chi2(2) 0.2694
Eq. 2 : Jarque-Bera LM Test = 2.2936 P-Value > Chi2(2) 0.3177
------------------------------------------------------------------------------

*** Overall System Non Normality Tests:
Ho: No Overall System Non Normality

*** Non Normality Tests:
- Jarque-Bera LM Test = 5.4681 P-Value > Chi2(2) 0.0650
- Doornik-Hansen LM Test = 4.9476 P-Value > Chi2(2) 0.0843
- Geary LM Test = 0.4365 P-Value > Chi2(2) 0.8039
- Anderson-Darling Z Test = -0.4223 P-Value>Z( 1.361) 0.9133
- D'Agostino-Pearson LM Test = 7.0244 P-Value > Chi2(2) 0.0298
------------------------------------------------------------------------------
*** Skewness Tests:
- Srivastava LM Skewness Test = 4.4358 P-Value > Chi2(1) 0.0352
- Small LM Skewness Test = 4.9358 P-Value > Chi2(1) 0.0263
- Skewness Z Test = -2.2217 P-Value > Chi2(1) 0.0263
------------------------------------------------------------------------------
*** Kurtosis Tests:
- Srivastava Z Kurtosis Test = 1.0160 P-Value > Z(0,1) 0.3096
- Small LM Kurtosis Test = 2.0887 P-Value > Chi2(1) 0.1484
- Kurtosis Z Test = 1.4452 P-Value > Chi2(1) 0.0742
------------------------------------------------------------------------------
Skewness Coefficient = -0.8848 - Standard Deviation = 0.4031
Kurtosis Coefficient = 3.8536 - Standard Deviation = 0.7879
------------------------------------------------------------------------------
Runs Test: (19) Runs - (19) Positives - (15) Negatives
Standard Deviation Runs Sig(k) = 2.8300 , Mean Runs E(k) = 17.7647
95% Conf. Interval [E(k)+/- 1.96* Sig(k)] = (12.2179 , 23.3115 )
------------------------------------------------------------------------------

Author

Emad Abd Elmessih Shehata
Assistant Professor
Agricultural Research Center - Agricultural Economics Research Institute - Egypt
Email: emadstat@hotmail.com
WebPage: http://emadstat.110mb.com/stata.htm
WebPage at IDEAS: http://ideas.repec.org/f/psh494.html
WebPage at EconPapers: http://econpapers.repec.org/RAS/psh494.htm

lmnsem Citation

Shehata, Emad Abd Elmessih (2012)

LMNSEM: "Stata Module to Compute Overall System Non Normality Tests after Structural Equation Modeling (SEM) Regressions"

Online Help:

lmasem, lmhsem, lmnsem, lmcovsem, r2sem,

lmareg3, lmhreg3, lmnreg3, lmcovreg3, r2reg3. (if installed).