factors in probit regression
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Hi to all of you,
I'm fitting an full factorial probit model from an experiment, and I've the independent variables as factors. The model is as follows: fit16<-glm(Sube ~ as.factor(CE)*as.factor(CEBO)*as.factor(Luz), family=binomial(link="probit"), data=experimento) but, when I took a look to the results I've obtained the following: glm(formula = Sube ~ CE * CEBO * Luz, family = binomial(link = "probit"), data = experimento) Deviance Residuals: Min 1Q Median 3Q Max -1.651e-06 -1.651e-06 1.651e-06 1.651e-06 1.651e-06 Coefficients: (3 not defined because of singularities) Estimate Std. Error z value Pr(>|z|) (Intercept) 6.991e+00 3.699e+04 0 1 CEexperimental 5.357e-09 4.775e+04 0 1 CENO -1.398e+01 4.320e+04 0 1 CEBOcombinado 4.948e-26 4.637e+04 0 1 CEBOolor 1.183e-25 4.446e+04 0 1 CEBOvisual 7.842e-26 5.650e+04 0 1 Luzoscuridad 3.383e-26 4.637e+04 0 1 CEexperimental:CEBOcombinado -6.227e-26 6.656e+04 0 1 CENO:CEBOcombinado -3.758e-26 5.540e+04 0 1 CEexperimental:CEBOolor -2.611e-25 6.865e+04 0 1 CENO:CEBOolor -5.252e-26 5.620e+04 0 1 CEexperimental:CEBOvisual -2.786e-09 7.700e+04 0 1 CENO:CEBOvisual 8.169e-15 6.334e+04 0 1 CEexperimental:Luzoscuridad -1.703e-25 6.304e+04 0 1 CENO:Luzoscuridad -1.672e-28 6.117e+04 0 1 CEBOcombinado:Luzoscuridad 1.028e-26 5.950e+04 0 1 CEBOolor:Luzoscuridad 9.212e-27 6.207e+04 0 1 CEBOvisual:Luzoscuridad NA NA NA NA CEexperimental:CEBOcombinado:Luzoscuridad 9.783e-26 8.744e+04 0 1 CENO:CEBOcombinado:Luzoscuridad -2.948e-26 7.959e+04 0 1 CEexperimental:CEBOolor:Luzoscuridad 1.573e-25 9.005e+04 0 1 CENO:CEBOolor:Luzoscuridad -2.111e-26 8.208e+04 0 1 CEexperimental:CEBOvisual:Luzoscuridad NA NA NA NA CENO:CEBOvisual:Luzoscuridad NA NA NA NA (Dispersion parameter for binomial family taken to be 1) Null deviance: 2.0853e+02 on 150 degrees of freedom Residual deviance: 4.1146e-10 on 130 degrees of freedom AIC: 42 Well, there are too many levels of the original factors lacking in this table. As an example, the factor CE has three levels (Undefined, Control, Experimental), but in the table there are only two of them (NO=undefined, Experimental=Experimental). I need to check the complete result, how can I obtain the effects for the remaining levels of the factors? Thanks, Pablo |
Re: factors in probit regression
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I need to quote David Winsemius on this one again: "The advancement of science would be safer if you knew what you were doing."
Note that the whole model screams at you that it is wrongly modeled. You are running a fully interacted model with factor variables. Thus, you have 19 regressors plus the baseline for 150 observations. Note that all your coefficients are insignificant with a z-value of 0 and a p-value of 1. This indicates that something is severely wrong with your model. And it is not difficult to tell what. If you look at the residual deviance, it is effectively zero. This means that you are overfitting the model. Your model explains fully (with no error), whether the dependent variable is a zero or a one. This may be meaningful in a descriptive but not in an inferential sense. Also, there are no "Control" coefficients or interactions because modeling three factor levels only requires two dummy variables. The other one becomes the omitted baseline that is absorbed in the intercept. That is, the intercept and the "plain" interaction terms capture that group. Please pick up an introductory econometrics book before continue. Best, Daniel
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Re: factors in probit regression
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On Oct 7, 2011, at 1:32 AM, Daniel Malter wrote: > Note that the whole model screams at you that it is wrongly modeled. > You are > running a fully interacted model with factor variables. Thus, you > have 19 > regressors plus the baseline for 150 observations. Note that all your > coefficients are insignificant with a z-value of 0 and a p-value of > 1. This > indicates that something is severely wrong with your model. And it > is not > difficult to tell what. If you look at the residual deviance, it is > effectively zero. This means that you are overfitting the model. > Your model > explains fully (with no error), whether the dependent variable is a > zero or > a one. This may be meaningful in a descriptive but not in an > inferential > sense. That may be true, but it does not mean that Pablo cannot get predictions from the model which was what was requested I'm not yet convinced that nothing can be done with this model. It may serve a useful purpose as a "saturated model" from which efforts at simplification might be attempted and from which deviations in the model and the predictions could be usefully considered. > > Also, there are no "Control" coefficients or interactions because > modeling > three factor levels only requires two dummy variables. The other one > becomes > the omitted baseline that is absorbed in the intercept. That is, the > intercept and the "plain" interaction terms capture that group. > Please pick > up an introductory econometrics book before continue. > > Best, > Daniel > > > garciap wrote: >> >> >> >> Well, there are too many levels of the original factors lacking in >> this >> table. As an example, the factor CE has three levels (Undefined, >> Control, >> Experimental), but in the table there are only two of them >> (NO=undefined, >> Experimental=Experimental). I need to check the complete result, >> how can I >> obtain the effects for the remaining levels of the factors? The predict function will produce estimates for any actual or hypothetical case when you supply a newdata argument with a dataframe that includes the same column names as the RHS of model. In regression with discrete variables alway one level that needs to be considered as part of the Intercept. In R that level is chosen as the first factor level. The Estimate offered for (Intercept) is actully the estimate for a case with CE, CEBO, and Luz all at their lowest factor level. Lowest depending on the spelling of their labels. You can make changes in that assignment. For advice about specific methods to do that in R, please first read the Posting Guide and include a much more complete description of the dataset such as produced by str(experimento). -- David. >> >> Thanks, >> >> Pablo >> > Hi to all of you, > > I'm fitting an full factorial probit model from an experiment, and > I've the > independent variables as factors. The model is as follows: > > > fit16<-glm(Sube ~ as.factor(CE)*as.factor(CEBO)*as.factor(Luz), > family=binomial(link="probit"), data=experimento) > > but, when I took a look to the results I've obtained the following: > > glm(formula = Sube ~ CE * CEBO * Luz, family = binomial(link = > "probit"), > data = experimento) > > Deviance Residuals: > Min 1Q Median 3Q Max > -1.651e-06 -1.651e-06 1.651e-06 1.651e-06 1.651e-06 > > Coefficients: (3 not defined because of singularities) > Estimate Std. Error z value > Pr(>|z|) > (Intercept) 6.991e+00 3.699e > +04 0 > 1 > CEexperimental 5.357e-09 4.775e > +04 0 > 1 > CENO -1.398e+01 4.320e > +04 0 > 1 > CEBOcombinado 4.948e-26 4.637e > +04 0 > 1 > CEBOolor 1.183e-25 4.446e > +04 0 > 1 > CEBOvisual 7.842e-26 5.650e > +04 0 > 1 > Luzoscuridad 3.383e-26 4.637e > +04 0 > 1 > CEexperimental:CEBOcombinado -6.227e-26 6.656e > +04 0 > 1 > CENO:CEBOcombinado -3.758e-26 5.540e > +04 0 > 1 > CEexperimental:CEBOolor -2.611e-25 6.865e > +04 0 > 1 > CENO:CEBOolor -5.252e-26 5.620e > +04 0 > 1 > CEexperimental:CEBOvisual -2.786e-09 7.700e > +04 0 > 1 > CENO:CEBOvisual 8.169e-15 6.334e > +04 0 > 1 > CEexperimental:Luzoscuridad -1.703e-25 6.304e > +04 0 > 1 > CENO:Luzoscuridad -1.672e-28 6.117e > +04 0 > 1 > CEBOcombinado:Luzoscuridad 1.028e-26 5.950e > +04 0 > 1 > CEBOolor:Luzoscuridad 9.212e-27 6.207e > +04 0 > 1 > CEBOvisual:Luzoscuridad NA NA > NA > NA > CEexperimental:CEBOcombinado:Luzoscuridad 9.783e-26 8.744e > +04 0 > 1 > CENO:CEBOcombinado:Luzoscuridad -2.948e-26 7.959e > +04 0 > 1 > CEexperimental:CEBOolor:Luzoscuridad 1.573e-25 9.005e > +04 0 > 1 > CENO:CEBOolor:Luzoscuridad -2.111e-26 8.208e > +04 0 > 1 > CEexperimental:CEBOvisual:Luzoscuridad NA NA > NA > NA > CENO:CEBOvisual:Luzoscuridad NA NA > NA > NA > > (Dispersion parameter for binomial family taken to be 1) > > Null deviance: 2.0853e+02 on 150 degrees of freedom > Residual deviance: 4.1146e-10 on 130 degrees of freedom > AIC: 42 > > > Well, there are too many levels of the original factors lacking in > this > table. As an example, the factor CE has three levels (Undefined, > Control, > Experimental), but in the table there are only two of them > (NO=undefined, > Experimental=Experimental). I need to check the complete result, how > can I > obtain the effects for the remaining levels of the factors? > > Thanks, > > Pablo > > > -- > View this message in context: http://r.789695.n4.nabble.com/factors-in-probit-regression-tp3879176p3881041.html > Sent from the R help mailing list archive at Nabble.com. > > ______________________________________________ > [hidden email] mailing list > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide http://www.R-project.org/posting-guide.html > and provide commented, minimal, self-contained, reproducible code. David Winsemius, MD West Hartford, CT ______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. |
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Dear Daniel,
I was thinking on what's wrong with you, and what it is supposed you're trying to critisize without knowing my work or any other detail. For your knowledge, the model I've sent was just an example; I've fitted 17 different models (no interactions, only one factor, etc) and of course this was not the best, it was another one with only two factors. I've noticed that there was something wrong with the model I've posted. Did your expect that I should post the results of 17 models? Further, if you run the analysis in some "commercial" statistical package, it is possible to change the design so there is no "baseline" and the effects can be tested. I don't need a economy book, I'm an ecologist. Please, think before post anything like your mail. Pablo PS. David, many thanks for your help. ______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. |
Re: factors in probit regression
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You can get an estimate for the omitted baseline category by not estimating the intercept. To do that, type "-1" on the right-hand side of the regression statement. If that was your actual question, the simple question, "How can I omit the baseline in a regression?," would have sufficed. Moreover, it is perfectly possible to obtain the estimates for the omitted category from the model you have showed. No offense, but this suggested that it was unclear to you why there is no estimate for the Control group in the first place and that it was possible to obtain the predictions you wanted from the model you provided. Hence, the suggestion to pick up an econometrics book seemed perfectly valid.
David is true that your model might be predictively valid. However, the residual deviance in your model would suggest that you should be able to predict whether the dependent variable is 0 or 1 with an accuracy that strongly approaches 100%. From my point of view, your predictive model would effectively be falsified if you can find an observation for which your model mispredicts the dependent variable. This is because the model you showed has essentially no margin of error. One reason for this may be that you use 20 DFs when you have 150 observations. As for criticizing you without knowing what you are doing. That is true, partially because you have not provided details and partially because I would have to wonder why you decided to provide the model you provided out of all the 17 you estimated. Finally, apologies to David for misquoting. However, I will venture to say that the statement is valid in this case. There is no indication in Pablo's original post whatsoever that he actually wants to predict from this model. And from an inferential point of view, his model is flawed. Best, Daniel
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