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I pose a very similar question to this, although I felt the advice given does not apply to my particular situation;

I am using logistic regression models for an animal habitat occupancy study, and all the predictor variables I am interested in contain >50% zeros (although they have a decent range of values in the higher percentiles). Can this cause bias or influence how I should interpret the estimated coefficients?

A 2-stage analysis, as suggested in the linked question, doesn't seem to make sense because all the predictors share this zero-inflated distribution.

Thanks for any insights

EDIT Clarifications suggested by Peter Flom;

Sample size ~ 500 (300 "0"s, 200 "1"s)

There are 5 IV's; a typical five-number summary looks like this;

min= 0.000 lower= 0.000 median=0.000 upper= 0.289 max= 16.887

Also, Mean= 0.468, SD= 1.467

correlations between the 5 IV's all absolute r < 0.3

The IV's are hectares of specific habitat types. Every sample has >0 hectare(s) for at least 1 of the IV's.

An example run of the model in R;

    Call:
    glm(formula = use ~ x.1 + x.2 + x.3 + x.4, family = binomial, 
        data = mydata)

Deviance Residuals: 
    Min       1Q   Median       3Q      Max  
-2.2338  -0.9312  -0.8679   1.3231   1.6432  

Coefficients:
        Estimate Std. Error z value Pr(>|z|)    
(Intercept) -0.78412    0.12814  -6.119 9.41e-10 ***
x.1          0.19866    0.06366   3.121  0.00181 ** 
x.2          0.06956    0.02618   2.657  0.00788 ** 
x.3          0.05238    0.02265   2.313  0.02074 *  
x.4         -0.09995    0.13814  -0.724  0.46935    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 634.10  on 473  degrees of freedom
Residual deviance: 611.18  on 469  degrees of freedom
AIC: 621.18

Number of Fisher Scoring iterations: 4
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    $\begingroup$ One of your biggest concerns could be the possible nonlinearity of the relationship due to distinctly different responses when the IVs are exact zeros compared to otherwise. One way to assess (and cope with) this is described in my answer at stats.stackexchange.com/a/4833. It proposes introducing additional variables that are indicators of zeros. (You do not necessarily have to take logs of the original IVs as well, which was discussed there only to respond to that particular question.) $\endgroup$ – whuber Jun 16 '14 at 22:46
  • $\begingroup$ @whuber I used the method described in the link, i.e.,glm(x.1+(ifelse(x.1==0,1,0)),family=binomial); and the differences in coefficient and standard error are very small (< 10%) in each case. I assume this means I don't have a serious non-linearity problem? Could you explain in more detail how the problem of non-linearity could be acute with zero-inflated predictors and how this "transformation" copes with it? $\endgroup$ – Dave M Jun 17 '14 at 16:59
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    $\begingroup$ Dave, sometimes--especially when an IV has a very positively skewed distribution--a true zero is a special value. It can, for instance, distinguish subjects that have a particular quantitative characteristic from those where that characteristic is meaningless (such as length of previous pregnancy). It can also comprehend a wide range of values that should be distinguished but were not, such as when you should really be using the log of the IV and have lumped all really tiny values into a single "zero" value. In either case, nonlinearity and heteroscedasticity are of diagnostic value. $\endgroup$ – whuber Jun 17 '14 at 18:57
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Logistic regression does not make any assumptions about the distribution of the independent variables (neither does OLS regression, but that's another post).

However, if there are a lot of variables and a lot of zero inflation, then I think the potential for complete or quasi-complete separation increases.

Another problem may be accuracy of estimates; as far as I know, the computed standard errors etc. will be correct, but I think they could well be large.

More details (the number of IVs; the sample size; the nature of the variables, the degree of correlation among the IVs) will help you get more detailed answers. Actually running the regression and posting results would also help.

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  • $\begingroup$ I added more detail to my post. I don't think there is a separation issue in the data. The results are about what I'd expect from comparing the descriptive statistics of the the 2 groups. $\endgroup$ – Dave M Jun 16 '14 at 22:17

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