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From |
John Antonakis <John.Antonakis@unil.ch> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Fwd: st: New package, -swain- : Correct small sample chi-square overidentification test |

Date |
Wed, 20 Mar 2013 16:43:50 +0100 |

error rates. I have requested an update to the description and the help file. Best, J. -------- Original Message --------

Date: Wed, 20 Mar 2013 13:11:53 +0100 From: John Antonakis <John.Antonakis@unil.ch> Reply-To: statalist@hsphsun2.harvard.edu To: statalist@hsphsun2.harvard.edu Hi: With the usual thanks to Kit Baum, a new package -swain- is available on SSC. This package should be interesting to those who estimate structural equation models via -sem- (using maximum likelihood). It might also be useful to those estimating models via two or three-stage least squares, which can be also estimated with -sem-.* Here is a description of -swain-: Correct small sample chi-square overidentification test after -sem- swain corrects the chi-square test of fit for structural equation models (with or without latent variables). The chi-square statistic is asymptotically correct; however, it does not behave as expected in small samples (Kenny & McCoach, 2003) and/or when the model is complex (Curren, Bollen, Paxton & Kirby, 2002). Thus, particularly in situations where the ratio of the number of parameters estimated to sample size is relatively small, the chi-square test will tend to overreject correctly specified models. To obtain a closer approximation to the distribution of the chi-square statistic, Swain (1975) developed a correction; this scaling factor, which converges to 1 asymptotically, is multiplied with the chi-square statistic. The resulting correction better approximates the chi-square distribution resulting in more appropriate Type 1 reject error. To install swain, simply type -ssc install swain- from the Stata command line. *How to estimate instrumental variable models via -sem-. E.g. 1 ivregress 2sls y (x = z1 z2) z3 can be estimated in -sem- as: sem (x <- z1 z2 z3) (y <- x z3) , cov(e.x*e.y) cov(e.x*e.y) allows cross equations disturbances of x and y to correlate (and it the Hausman test). E.g. 2 reg3 (y = x1 z3) (x = z1 z2 z3 x2) (x2 = z4 z3) can be estimated in -sem- as: sem (y <- x1 z3) (x <- z1 z2 z3 x2) (x2 <- z4 z3), cov(e._OEn, unstructured) The cov option above allows all cross-equation disturbances of endogenous variables correlate. Thus, the Hausman test is the Wald test: test (_b[cov(e.y,e.x1):_cons] = 0) (_b[cov(e.y,e.x2):_cons]=0) (_b[cov(e.x1,e.x2):_cons]=0) Note, the Hansen-Sargan overidentification statistic in 2sls is the chi-square test of fit in sem (reported as the "LR test of model vs. saturated model" on the bottom of the output). In small sample size situations where there are many parameters to be estimated, -swain- will correct this overidentification statistic. Another advantage of using -sem- is that there are score tests (modification indices or Langrange Multiplier tests) available after estimation (-estat mindices-) that will identify model constraints that are inconsistent with the data. Best, J. -- __________________________________________ John Antonakis Professor of Organizational Behavior Director, Ph.D. Program in Management Faculty of Business and Economics University of Lausanne Internef #618 CH-1015 Lausanne-Dorigny Switzerland Tel ++41 (0)21 692-3438 Fax ++41 (0)21 692-3305 http://www.hec.unil.ch/people/jantonakis Associate Editor The Leadership Quarterly __________________________________________ * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/faqs/resources/statalist-faq/ * http://www.ats.ucla.edu/stat/stata/ * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/faqs/resources/statalist-faq/ * http://www.ats.ucla.edu/stat/stata/

**References**:**st: New package, -swain- : Correct small sample chi-square overidentification test***From:*John Antonakis <John.Antonakis@unil.ch>

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