The factor analysis models and estimation methods for continuous (i.e., interval or ratio scale) data are not appropriate for item-level data that are categorical in nature. The authors provide a brief review and synthesis of the item factor analysis estimation literature for categorical data (e.g., 0-1 type response scales). Popular categorical item factor analysis models and estimation methods found in the structural equation modeling and item response theory literatures are presented. Two Monte Carlo simulation studies are conducted and revealed: (1) Similar parameter estimates have been obtained from the SEM and IRT parameterizations. Even with a small sample and the IRT estimates converted to SEM parameters, the MWLSc, and MML/EM results are strikingly similar. But in small sample size and long test, WLSc did not obtain the convergence parameter estimations, although in short test, WLSc estimates have been obtained, the estimates are consistently more discrepant than those produced by the other estimation techniques. (2) The precise of the estimators enhances as the quantity of the sample increases. (3) The precise of item factor load and of item difficulty parameter is influenced by the test length. (4) The precise of item factor load and of item discrimination parameter is influenced by the size of the whole factor load (discrimination). (5) The distribution of the threshold of test item affects the precise of the parameter estimate, and item discrimination is the most sensitive parameter to the threshold. (6) In whole, the precise of item parameter estimate in SEM framework is higher than that in IRT framework. Both structural equation modeling (SEM) and item response theory (IRT) can be used for factor analysis of dichotomous item responses. In this case, the measurement models of both approaches are formally equivalent. They were refined within and across different disciplines, and make complementary contributions to central measurement problems encountered in almost all empirical social science research fields. The authors conclude with considerations for categorical item factor analysis and give some advice for applied researchers.