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The non-normal data which is highly inflated to zero responses is called zero-inflated data. This type of data can be seen often in social science studies. However, structural equation modeling for zero-inflated data is less studied in terms of the structural model. This study discusses two-part factor model and general factor model for the structural path model when zero-inflated data is included in the path. A Monte Carlo simulation study was conducted to compare a two-part factor model and a single factor model. The effectiveness of data transformation was also examined based on the single factor model. Two-part factor model was superior to other approaches in some conditions. Other recommended approaches were also discussed.