GenLin
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I’m curious about the underlying design specification for GenLin. I was going to use it to do a nominal, multinomial regression, such as what NomReg does, but as I read the documentation GenLin will do ordinal regression (like Plum) but
will not do nominal regression, which, frankly, surprised me. I don’t think I misread the documentation but I certainly may have. What I’m curious about is whether nominal regression presents a different computational or programming logic problem from the
problem presented by the included Distribution-Link combinations. Gene Maguin |
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Hi Gene. I'm reading the GENLIN documentation the same way you are--i.e., it cannot estimate the same model as NOMREG. But it looks like GENLINMIXED can, if that helps you. See the Target Options section here:
http://pic.dhe.ibm.com/infocenter/spssstat/v20r0m0/index.jsp?topic=%2Fcom.ibm.spss.statistics.help%2Fsyn_genlinmixed_overview.htm HTH.
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Bruce Weaver bweaver@lakeheadu.ca http://sites.google.com/a/lakeheadu.ca/bweaver/ "When all else fails, RTFM." PLEASE NOTE THE FOLLOWING: 1. My Hotmail account is not monitored regularly. To send me an e-mail, please use the address shown above. 2. The SPSSX Discussion forum on Nabble is no longer linked to the SPSSX-L listserv administered by UGA (https://listserv.uga.edu/). |
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In reply to this post by Maguin, Eugene
Gene, Suppose you want to fit a cumulative logit model for an ordinal response with 4 categories, along with two continuous predictors. The cumulative logit model would be constructed such that the probabilities (pr1, pr2, pr3, pr4) are a function of the linear predictors (eta1, eta2, eta3) as follows:
pr1 = 1 / [1 + exp(eta1)] pr2 = 1 / [1 + exp(eta2)) - 1 / (1 + exp(eta1)] pr3 = 1 / [1 + exp(eta3)) - 1 / (1 + exp(eta2)] pr4 = 1 - 1 / [1 + exp(eta3)] where eta1 = beta1_0 + beta1*x1 + beta2*x2 eta2 = beta2_0 + beta1*x1 + beta2*x2 eta3 = beta3_0 + beta1*x1 + beta2*x2 Notice that the linear predictors (eta1 through eta3) are permitted to have varying intercepts as denoted by different names (e.g., beta1_0, beta2_0), but the slopes are constrained to be equal (e.g., beta1). Also notice the cumulative nature of how the probabilities are constructed. Of note, requiring the slopes to be equal is based on the the proportional odds assumption.
On the other hand, the generalized logit model would be constructed as follows: pr1 = exp(eta1) / [1 + exp(eta1) + exp(eta2) + exp(eta3)] pr2 = exp(eta2) / [1 + exp(eta1) + exp(eta2) + exp(eta3)]
pr3 = exp(eta3) / [1 + exp(eta1) + exp(eta2) + exp(eta3)] pr4 = 1 / [1 + exp(eta1) + exp(eta2) + exp(eta3)] where eta1 = beta1_0 + beta1_1*x1 + beta1_2*x2
eta2 = beta2_0 + beta2_1*x1 + beta2_2*x2 eta3 = beta3_0 + beta3_1*x1 + beta3_2*x2 Above you will find that the intercepts *and* slopes are permitted to vary across linear predictors and the probabilities are constructed in a non-cumulative way.
There is, of course, no reason to be limited to either extreme. You could fit a partial proportional odds model so long as the statistical procedure allowed it, for example. Needless to say, either model above can accommodate random effects. It's unlikely, however, that any procedure in SPSS will allow those random effects to be correlated for the models specified above. That's an SPSS limitation you would have to accept.
HTH. Ryan On Mon, Feb 24, 2014 at 10:24 AM, Maguin, Eugene <[hidden email]> wrote:
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In reply to this post by Bruce Weaver
Hi Gene,
The underlying nominal regression and ordinal regression algorithms are, indeed, non-trivially different**. When Genlin was introduced, the intention may have been to introduce the procedure, and then add nominal regression models at a later date if there was enough user interest. Presumably there was not, and then when GENLINMIXED was introduced (as Bruce points out), it covered both types of models. Alex ** See, for example, the sections on the Nominal multinomial distribution and Ordinal multinomial distributions under the generalized linear mixed models algorithms: http://pic.dhe.ibm.com/infocenter/spssstat/v22r0m0/topic/com.ibm.spss.statistics.algorithms/alg_glmm.htm From: Bruce Weaver <[hidden email]> To: [hidden email], Date: 02/24/2014 11:33 AM Subject: Re: GenLin Sent by: "SPSSX(r) Discussion" <[hidden email]> Hi Gene. I'm reading the GENLIN documentation the same way you are--i.e., it cannot estimate the same model as NOMREG. But it looks like GENLINMIXED can, if that helps you. See the Target Options section here: http://pic.dhe.ibm.com/infocenter/spssstat/v20r0m0/index.jsp?topic=%2Fcom.ibm.spss.statistics.help%2Fsyn_genlinmixed_overview.htm HTH. Maguin, Eugene wrote > I'm curious about the underlying design specification for GenLin. I was > going to use it to do a nominal, multinomial regression, such as what > NomReg does, but as I read the documentation GenLin will do ordinal > regression (like Plum) but will not do nominal regression, which, frankly, > surprised me. I don't think I misread the documentation but I certainly > may have. What I'm curious about is whether nominal regression presents a > different computational or programming logic problem from the problem > presented by the included Distribution-Link combinations. > > Gene Maguin |
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Hi Alex, I don't see why they [IBM-SPSS] would abandon adding a glogit link to GENLIN since AFAIA GENLINMIXED is incapable of fitting GEE-Type models. Ryan Sent from my iPhone
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That's a good point, Ryan. I was
forgetting that GEE was wrapped up inside GENLIN instead of exposed as
a separate procedure.
Alex From: Ryan Black <[hidden email]> To: [hidden email], Date: 02/25/2014 07:48 PM Subject: Re: GenLin Sent by: "SPSSX(r) Discussion" <[hidden email]> Hi Alex, I don't see why they [IBM-SPSS] would abandon adding a glogit link to GENLIN since AFAIA GENLINMIXED is incapable of fitting GEE-Type models. Ryan Sent from my iPhone On Feb 25, 2014, at 7:24 PM, Alex Reutter <areutter@...> wrote: Hi Gene, The underlying nominal regression and ordinal regression algorithms are, indeed, non-trivially different**. When Genlin was introduced, the intention may have been to introduce the procedure, and then add nominal regression models at a later date if there was enough user interest. Presumably there was not, and then when GENLINMIXED was introduced (as Bruce points out), it covered both types of models. Alex ** See, for example, the sections on the Nominal multinomial distribution and Ordinal multinomial distributions under the generalized linear mixed models algorithms: http://pic.dhe.ibm.com/infocenter/spssstat/v22r0m0/topic/com.ibm.spss.statistics.algorithms/alg_glmm.htm From: Bruce Weaver <bruce.weaver@...> To: [hidden email], Date: 02/24/2014 11:33 AM Subject: Re: GenLin Sent by: "SPSSX(r) Discussion" <[hidden email]> Hi Gene. I'm reading the GENLIN documentation the same way you are--i.e., it cannot estimate the same model as NOMREG. But it looks like GENLINMIXED can, if that helps you. See the Target Options section here: http://pic.dhe.ibm.com/infocenter/spssstat/v20r0m0/index.jsp?topic=%2Fcom.ibm.spss.statistics.help%2Fsyn_genlinmixed_overview.htm HTH. Maguin, Eugene wrote > I'm curious about the underlying design specification for GenLin. I was > going to use it to do a nominal, multinomial regression, such as what > NomReg does, but as I read the documentation GenLin will do ordinal > regression (like Plum) but will not do nominal regression, which, frankly, > surprised me. I don't think I misread the documentation but I certainly > may have. What I'm curious about is whether nominal regression presents a > different computational or programming logic problem from the problem > presented by the included Distribution-Link combinations. > > Gene Maguin |
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Hi Alex, IF, and this is a big IF, GENLIN allows one to incorporate an interaction term as the SUBJECT identifier, along with a non-independent correlation structure, then the GEE multinomial (unordered) logistic regress model can be reparameterized as a GEE multivariate binomial logistic regression.
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