help: lmhsem dialog:

Title

lmhsem: Overall System Heteroscedasticity Tests after (SEM) Regressions

Syntax

lmhsem

Description

lmhsem computes overall system Heteroscedasticity tests, after:

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

lmhsem calculates single Equation Heteroscedasticity:

- Engle LM ARCH Test.

- Hall-Pagan LM Test: E2 = Yh.

- Hall-Pagan LM Test: E2 = Yh2.

- Hall-Pagan LM Test: E2 = LYh2.

lmhsem calculates overall system Heteroscedasticity:

- Breusch-Pagan LM Test.

- Likelihood Ratio LR Test.

Saved Results

lmhsem saves the following in r():

Scalars

r(lmhlm) Breusch-Pagan LM Test

r(lmhlmp) Breusch-Pagan LM Test P-Value

r(lmhlr) Likelihood Ratio LR Test

r(lmhlrp) Likelihood Ratio LR Test P-Value

e(mharch_#) Engle LM ARCH Test for eq.i
e(mharchp_#) Engle LM ARCH Test for eq.# P-Value
e(lmhhp1_#) Hall-Pagan LM Test E2 = Yh for eq.#
e(lmhhp1p_#) Hall-Pagan LM Test E2 = Yh for eq.# P-Value
e(lmhhp2_#) Hall-Pagan LM Test E2 = Yh2 for eq.#
e(lmhhp2p_#) Hall-Pagan LM Test E2 = Yh2 for eq.# P-Value
e(lmhhp3_#) Hall-Pagan LM Test E2 = Yh3 for eq.#
e(lmhhp3p_#) Hall-Pagan LM Test E2 = Yh3 for eq.# P-Value

Examples

in this example FIML will be used as follows:

clear all

sysuse lmhsem.dta , clear

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

lmhsem

return list

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

db lmhsem

. clear all
. sysuse lmhsem.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

. lmhsem

=================================================
* System Heteroscedasticity Tests (ml)
=================================================
*** Single Equation Heteroscedasticity Tests:
Ho: Homoscedasticity - Ha: Heteroscedasticity

Eq. 1 : Engle LM ARCH Test: E2 = E2_1 = 0.0319 P-Value > Chi2(1) 0.8582
Eq. 1 : Hall-Pagan LM Test: E2 = Yh = 3.2488 P-Value > Chi2(1) 0.0715
Eq. 1 : Hall-Pagan LM Test: E2 = Yh2 = 3.5925 P-Value > Chi2(1) 0.0580
Eq. 1 : Hall-Pagan LM Test: E2 = LYh2 = 2.9051 P-Value > Chi2(1) 0.0883
------------------------------------------------------------------------------
Eq. 2 : Engle LM ARCH Test: E2 = E2_1 = 0.6860 P-Value > Chi2(1) 0.4075
Eq. 2 : Hall-Pagan LM Test: E2 = Yh = 1.0007 P-Value > Chi2(1) 0.3171
Eq. 2 : Hall-Pagan LM Test: E2 = Yh2 = 0.8447 P-Value > Chi2(1) 0.3581
Eq. 2 : Hall-Pagan LM Test: E2 = LYh2 = 1.1165 P-Value > Chi2(1) 0.2907
------------------------------------------------------------------------------
*** Overall System Heteroscedasticity Tests:
Ho: No Overall System Heteroscedasticity

- Breusch-Pagan LM Test = 0.9775 P-Value > Chi2(1) 0.3228
- Likelihood Ratio LR Test = 1.0067 P-Value > Chi2(1) 0.3157
------------------------------------------------------------------------------

References

Greene, William (1993)
"Econometric Analysis",
2nd ed., Macmillan Publishing Company Inc., New York, USA.; 492-493.

Greene, William (2007)
"Econometric Analysis",
6th ed., Macmillan Publishing Company Inc., New York, USA.; 534-536.

Judge, Georege, W. E. Griffiths, R. Carter Hill, Helmut Lutkepohl, & Tsoung-Chao Lee(1985)
"The Theory and Practice of Econometrics",
2nd ed., John Wiley & Sons, Inc., New York, USA; 494.

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

lmhsem Citation

Shehata, Emad Abd Elmessih (2012)

LMHSEM: "Stata Module to Compute Overall System Heteroscedasticity Tests after Structural Equation Modeling (SEM) Regressions"

Online Help:

lmasem, lmhsem, lmnsem, lmcovsem, r2sem,

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