人類學科裡的反應變項通常是二元或順序的，而不是等距。由於類別的試題反應跟其所欲測量的潛在特質的關係不會是線性的，於是就發展了試題反應理論來描述它們之間的非線性關係。另一種類別資料分析方法，試圖建立潛在連續反應與所欲測量的潛在特質的線性關係，然後透過閾值模式將潛在連續反應轉化為觀察的類別反應。當結構方程模式裡的測量模式中的試題反應與潛在特質之間的關係是非線性時，就可稱為非線性結構模式。其參數可用貝氏（WinBUGS軟體）或非貝氏（Mplus軟體）來估計。從模擬研究裡，我們發現雖然這兩種軟體都可以很精確的估計參數，但當測驗短時，WinBUGS 的估計效果比Mplus好。如果原始試題反應不可得的話，使用可能值的作法可以有效估計內衍變項和外衍變項間的結構參數，但是最大概似估計的作法嚴重低估結構參數，因為它完全沒有考慮測量誤差。兩個實證的例子說明了非線性結構模式和可能值作法的意涵與應用。

Response variables in the human sciences are often binary or ordinal rather than interval. Because the relationship between categorical item responses and their underlying latent traits cannot be linear, item response theory (IRT) models have been developed to describe the nonlinear relationship between them. Another approach to categorical data is to establish linear relationship between latent continuous responses and their underlying latent traits and convert latent continuous responses to observed categorical item responses via threshold models. When the relationships between item responses and their underlying latent traits are nonlinear in the measurement part of structural equation modeling (SEM), the resulting SEM can be called nonlinear SEM (NSEM), to emphasize the nonlinear relationships between item responses and the underlying latent traits. Parameters in NSEM can be estimated using the Bayesian (WinBUGS) or non-Bayesian (Mplus) approaches. In a series of simulations, it was found that although both WinBUGS and Mplus can recover parameters in NSEM very well, WinBUGS slightly out-performs Mplus when tests are short. When original item responses are not accessible, the use of the plausible-value approach can recover the structural parameters for exogenous and endogenous variables as satisfactorily as WinBUGS and Mplus can when original responses are accessible. However, the use of the maximum likelihood estimate approach underestimates the structural parameters substantially because the measurement error is ignored completely. Depression and resource planning are two empirical examples that illustrate the implications and applications of NSEM and the plausible-value approach.