Why does the number of rows change during AIC in R? How to ensure that this doesn’t happen?

From the Warnings section of ?step:

The model fitting must apply the models to the same dataset. This may be a problem if there are missing values and R’s default of na.action = na.omit is used. We suggest you remove the missing values first.

So you should do:

no.na.data <- na.omit(data[c(predictors, response)])
model <- lm(formula=as.formula(paste(paste(response,'~', sep=''),
                                     paste(predictors,collapse='+'), sep='')),

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