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From |
Jeremy Reynolds <jeremyr@uga.edu> |

To |
"statalist@hsphsun2.harvard.edu" <statalist@hsphsun2.harvard.edu> |

Subject |
st: Paul Allison's SEM model with fixed effects, reciprocal effects, and lagged predictors |

Date |
Tue, 1 Oct 2013 09:27:26 -0400 |

Dear Statalist, On June 29th, 2013, I asked for help estimating an SEM model that contains fixed effects, reciprocal effects, and lagged predictors. The model was suggested by Paul Allison (see references at the end of this post). I thought others might be interested in the solution, so I have posted it below. Jeremy The models below estimate the relationship between the proportion of women in an occupation (pf*) and the occupation's median wage (mdwgf*). They contains fixed effects (FE) and lagged measures of the dependent variable. They also contain a correlation between the error term in the first equation and all future values of the cross-lagged IV (in this case there is only one future value). To add this special correlation, we have to play a little trick on stata that was suggested by Richard Williams. Specifically, Stata does does not permit correlations between exogenous variables and error variables (SEM manual pg 240). Howevever, mathematically, error terms are just special cases of latent variables. Therefore, we set the covariance for the error term in the first equation (e.g., e.pf2) to zero using the cov() option. This prevents it from covarying with anyting and effectively removes it from the model. The latent variable ERR1 takes the place of the removed error term and is only allowed to covary with future values of the cross-lagged variable (e.g., mdwgf3). This special new variable should not be correlated with any other exogenous variables including the fixed effects (FE) These additional constraints on how ERR1 correlates with other variables are specified in the cov() option. Note: The results below match Allison's results with MPlus, but to match his SAS results, the method(mlmv) option must be removed. ************************************ *Median Wage, Proportion Female Example ************************************ use "http://www.statisticalhorizons.com/wp-content/uploads/occ.dta";, clear #delimit ; sem (pf2 <- mdwgf1@c1 pf1@c2 FE@1 ERR1@1) // fixed effects and latent var (ERR1) to replace error term (pf3 <- mdwgf2@c1 pf2@c2 FE@1) (pf4 <- mdwgf3@c1 pf3@c2 FE@1), cov(e.pf2@0) // covariance of error term set to zero to remove it from the model cov(ERR1*_oexogenous@0 ERR1*FE@0 ERR1*mdwgf3) // ERR1 should only correlate with future values of cross-lagged IV nocapslatent latent(FE ERR1) method(mlmv); #delimit cr *Model 2 (2nd half of model) #delimit ; sem (mdwgf2 <- pf1@c1 mdwgf1@c2 FE@1 ERR1@1) // fixed effects and latent var (ERR1) to replace error term (mdwgf3 <- pf2@c1 mdwgf2@c2 FE@1) (mdwgf4 <- pf3@c1 mdwgf3@c2 FE@1), cov(e.mdwgf2@0) // covariance of error term set to zero to remove it from the model cov(ERR1*_oexogenous@0 ERR1*FE@0 ERR1*pf3) // ERR1 should only correlate with future values of cross-lagged IV nocapslatent latent(FE ERR1) method(mlmv); #delimit cr The model estimated by the code above is described in the works below. http://www.statisticalhorizons.com/wp-content/uploads/2012/01/Causal-Inference.pdf England et al. Social Science Research 36: 2007 Fixed Effects Regression Models Using SAS, 2005 by Paul Allison Fixed Effects Regression Models, Sage green book # 160, 2009 by Paul Allison -- ******************** Dr. Jeremy Reynolds Associate Professor Undergraduate Coordinator Department of Sociology 116 Baldwin Hall University of Georgia Athens, GA 30602-1611 Phone: (706) 583-8072 Web: http://uga.edu/soc/people/faculty/reynolds_jeremy.php Fax: (706) 542-4320 * * 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/

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