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factors in probit regression

5 messages · garciap, David Winsemius, "Pablo García Díaz" +1 more

garciap
# 
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

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Daniel Malter
# 
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
garciap wrote:
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


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David Winsemius
#
On Oct 7, 2011, at 1:32 AM, Daniel Malter wrote:

            

      
      
      
    

        
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.

            

      
      
      
    

        
snipped duplicate output

            

      
      
      
    

        
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).

  
    

      
      
    

  


  


      

    

    

      
      

        


  

        

      "Pablo García Díaz"
    

    

      
      #
    

  


  

      
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.

  
  


  


      

    

    

      
      

        


  

        

      Daniel Malter
    

    

      
      #
    

  


  

      
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

        
garciap wrote:

            

      
      
      
    

        

      
      
    

        
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