tag:blogger.com,1999:blog-3240271627873788873.post4345387832494422608..comments2024-03-26T06:46:11.752-04:00Comments on Doing Bayesian Data Analysis: Bayesian variable selection in multiple linear regression: Model with highest R^2 is not necessarily highest posterior probabilityJohn K. Kruschkehttp://www.blogger.com/profile/17323153789716653784noreply@blogger.comBlogger4125tag:blogger.com,1999:blog-3240271627873788873.post-44368686870082850402016-07-22T01:34:21.551-04:002016-07-22T01:34:21.551-04:00I suppose one could overcome the limitations you m...I suppose one could overcome the limitations you mention by not doing variable selection at all!<br /><br />Lets say I only put the inclusion criteria on cross-loadings. I leave target loadings (i.e., loadings of indicator items of the factors they are designed to measure) as is. Now lets say the parameters I am interested in are those at the latent level. i.e., latent correlations. It strikes me that the overall summary results for the latent correlation will be a weighted average of all candidate models for cross-loadings where the weight will be determined by model probabilities. To be honest this might be preferable to model selection is self!Philiphttps://www.blogger.com/profile/11211371547658652661noreply@blogger.comtag:blogger.com,1999:blog-3240271627873788873.post-52251920803814078192016-07-20T18:45:20.402-04:002016-07-20T18:45:20.402-04:00This comment has been removed by the author.Philiphttps://www.blogger.com/profile/11211371547658652661noreply@blogger.comtag:blogger.com,1999:blog-3240271627873788873.post-20412644132049501622016-07-20T09:38:58.625-04:002016-07-20T09:38:58.625-04:00@Philip:
Absoultely, in principle you can put in...@Philip: <br /><br />Absoultely, in principle you can put inclusion coefficients on latent factors just like manifest variables. <br /><br />But you've gotta be very careful to do it all sensibly, and then you've gotta battle all the particulars of implementing it. These considerations are discussed in sections 18.4.4 and 18.4.5 of DBDA2E.<br />John K. Kruschkehttps://www.blogger.com/profile/17323153789716653784noreply@blogger.comtag:blogger.com,1999:blog-3240271627873788873.post-90807562707038196402016-07-19T21:13:39.197-04:002016-07-19T21:13:39.197-04:00Could this be modified in the case of Bayes confir...Could this be modified in the case of Bayes confirmatory factor analysis to reduce cross-loadings to a parsimonious set. <br /><br />What I am thinking is starting with a full ESEM model (i.e., all cross-loadings) and place inclusion coefficents just on the cross loadings. So for example lets say we have a two factor latent model with all cross-loadings, a indicator item y1 might have a JAGS specification like (where t = 1 in this case representing item y1):<br /><br />y[i,t] ~ dnorm(condmn[i,t], invsig2[t])<br />condmn[i,t] <-mu[t] + fload1[t]*fscore[i,1] + fload2[t]*fscore[i,2]<br /><br />Where fload1 represents the loading on the latent factor the indicator item is supposed to load on and fload2 is the crossloading. Could we modify this as per you post such that the code becomes:<br /><br />y[i,t] ~ dnorm(condmn[i,t], invsig2[t])<br />condmn[i,t] <-mu[t] + fload1[t]*fscore[i,1] + delta[t]*fload2[t]*fscore[i,2]<br />Philiphttps://www.blogger.com/profile/11211371547658652661noreply@blogger.com