# "Zero-inflated continuous covariates", Can they cause problems in logistic regression?

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

• 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.)
– whuber
Commented Jun 16, 2014 at 22:46
• @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? Commented Jun 17, 2014 at 16:59
• 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.
– whuber
Commented Jun 17, 2014 at 18:57