We develop and discuss residual analysis to evaluate the fit of alternative Rasch counts (RC) item response theory (IRT) models. The most general model proposed is the zero-inflated negative Binomial (ZIBN) IRT which include the RC Poisson IRT model as a special case. Additionally, new methods to estimate the parameters of the model considering penalized maximum likelihood using the Rigby and Stasinopoulos algorithm and integrated nested Laplace approximation (INLA) with a Bayesian approach are introduced, and randomized quantile residuals are proposed for item-fit analysis. To illustrate our approach, we use data from a selective attention test where 228 respondents from 3rd and 4th grade had to cross out two digits in 20 blocks each containing three lines with randomly arranged digits and letters. By considering the estimation methods we show that the residual analysis using violin plots works relatively well to identify the best model for the data.