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There are a great number of research studies that discussed dimensionality assessment with various structure complexity magnitude, i.e., the number of items with ‘cross-loadings,’ or those that required knowledge on multiple dimensions. However, previous studies did not discuss the effect of structure complexity magnitude on item parameter estimation. In addition, many times when factor loadings exhibit ‘small’ cross loadings, the data are treated as having a simple structure, ignoring the small cross-loading of some items. In this study we will investigate the impact of structure complexity magnitude of the data, the degree of cross-loading on secondary dimension and model specification (mis-specified simple structure model when data are truly complex) on item parameter estimation in Multidimensional Item Response Theory (MIRT).