I am carrying out glms on count data, several of my variables consist of largely of zero values, i was previously told to exclude these variables as it would reduce the model fit. I can't find a reference or source that suggests this approach is accepted.
Is this a valid approach and can anyone suggest a reference?
Typically zero-inflated predictors are not problematic for the statistics. In a regression, the distribution assumptions for hypothesis testing are related to the independent variable or the residuals (as in OLS, we want the residuals to be normally distributed). That being said, when thinking about an increase in 1 unit of the predictor may be misleading or confusing when the predictor doesn't really operate in that way - a 1 unit is rarely found in real life. An alternative could be to make the variable binary (e.g. 0 for predictor=0, 1 for predictor>0) or ordinal (e.g. 0 for predictor=0, 1 for predictor>0 and <k, 2 for predictor >=k). That could result in you losing some information, but it may be more interpretable and more reflective of the data generating process.
This relates to a question about outliers Which are outliers? and whether they should be removed.
Whether or not to remove certain extreme values depends on whether or not they are supposed to be part of the population that you wish to model.
What is the reason for these zero values? Are these zero's part of the population of interest (then you should keep them included), or are they deviations like errors in the measurement or sampling mechanism (then you can exclude them)?
Asside from this issue, it is noteworthy that apparently you have some source of error in your regressor variables (often called "independent" variables but not always truly independent). This makes that a model like GLM might not be suitable (it depends on what your goals are, do you want to test some 'mechanistic model' that is used to build scientific knowledge or do you want to fit some 'statistical model' that is used to make predictions based on previous data?)
