مقایسهٔ روش‌ها

	مدل پروبیت دو متغیره	رگرسیون لجستیک چندجمله‌ای (Multinomial Logistic Regression)	رگرسیون لجستیک ترتیبی (Ordered Logit/Probit)	مدل رگرسیون پروبیت
حوزه	اقتصادسنجی	اقتصادسنجی	اقتصادسنجی	اقتصادسنجی
خانواده	Regression model	Regression model	Regression model	Regression model
سال پیدایش	1970	1974	1980	2018
پدیدآور	J. R. Ashford & R. R. Sowden	McFadden	McCullagh (proportional odds / cumulative model)	Greene (textbook treatment); classical discrete-choice modelling
نوع	Maximum-likelihood binary outcome model	Multinomial logistic regression	Cumulative ordinal regression	Binary discrete-choice model
منبع بنیادین	Ashford, J. R., & Sowden, R. R. (1970). Multi-variate probit analysis. Biometrics, 26(3), 535–546.	McFadden, D. (1974). Conditional Logit Analysis of Qualitative Choice Behavior. In P. Zarembka (Ed.), Frontiers in Econometrics (pp. 105-142). Academic Press. ISBN: 978-0127761503	McCullagh, P. (1980). Regression Models for Ordinal Data. Journal of the Royal Statistical Society: Series B, 42(2), 109-142.	Greene, W. H. (2018). Econometric Analysis (8th ed.). Pearson. ISBN: 978-0134461366
نام‌های دیگر	Bivariate Binary Probit, Joint Probit Model, Two-Equation Probit, İki Değişkenli Probit	multinomial logistic regression, polytomous logistic regression, softmax regression, Çok Kategorili Lojistik Regresyon	ordinal logistic regression, proportional odds model, cumulative logit model, ordered probit	probit regression, normit model, Probit Modeli
مرتبط	3	5	4	5
خلاصه	The Bivariate Probit Model, introduced by Ashford and Sowden (1970), jointly estimates two binary outcome equations whose error terms are allowed to be correlated. By modeling both outcomes simultaneously under a bivariate normal distribution, it corrects for the dependence between decisions that separate probit regressions would ignore, producing consistent and efficient parameter estimates for researchers studying interrelated binary choices.	Multinomial logistic regression is a maximum-likelihood method for a nominal (unordered) dependent variable with more than two categories. Building on McFadden's 1974 treatment of qualitative choice, it gives each category its own set of coefficients relative to a reference category.	Ordered logit is a cumulative regression model for an ordinal dependent variable, fitting a logit (or probit) link to the cumulative category probabilities. Developed in McCullagh's 1980 treatment of regression models for ordinal data, it is the standard tool for Likert-scale, rating, and ranked outcomes.	The probit model is a regression method for a binary (0/1) outcome that maps a linear index of the predictors through the standard normal cumulative distribution function to produce a probability. It is a classical discrete-choice alternative to logistic regression, developed in standard econometrics treatments such as Greene's Econometric Analysis (2018).