Weighted least squares (WLS), weighted least squares mean-and-variance-adjusted (WLSMV), unweighted least squares mean-and-variance-adjusted (ULSMV), maximum likelihood (ML), robust maximum likelihood (MLR) and Bayesian estimation methods were compared in mixed item response type data via Monte Carlo simulation. The percentage of polytomous items, distribution of polytomous items, categories of polytomous items, average factor loading, sample size and test length conditions were manipulated. ULSMV and WLSMV were found to be the more accurate methods under all simulation conditions. All methods except WLS had acceptable relative bias and relative standard error bias. No method gives accurate results with small sample sizes and low factor loading, however, the ULSMV method can be recommended to researchers because it gives more appropriate results in all conditions.