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There are some distributional assumptions about the error, but these cannot be tested in a formal way (as far as I know). There is also a parallel regression assumption, which is frequently violated. Long and Freese's categorical dependent variables book describes an approximate LR and a Wald (aka Brant) test (and provides Stata code).

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I have encountered this problem recently and have not found many sources which explain this so I thought I would answer. The interaction effect in a non-linear model is possible to compute but it is tricky as it is not equal to the marginal effect on the interaction term. Say you have the probit model $E(y|x_1,x_2)=\Phi(\beta_1 x_1 + \beta_2 x_2 + \beta_{12}... 4 It looks to me that you are looking for the "partial" version of proportional odds. Reference: R. S. Society, “Partial Proportional Odds Models for Ordinal Response Variables,” vol. 39, no. 2, pp. 205–217, 1999. If in the "standard" ordered logit (or proportional odds), the cumulative probability is modeled as $$P(Y > j | X_i) = \frac{1}{1 + \exp(-\... 4 The documentation for car::Anova does not indicate that it works with clm or clmm objects. From your examples, it appears it can have some unusual behavior. My solution is to use RVAideMemoire::Anova.clm. So, for your EDIT 2 example: if(!require(RVAideMemoire)){install.packages("RVAideMemoire")} if(!require(car)){install.packages("car")} library(car) ... 3 Here is some R code simulating data, fitting a model by standard maximum likelihood methods assuming that the counts follow a multinomial distribution, and comparing observed and fitted expected observed counts. # Simulate the data generating process set.seed(1) n <- 500 sex <- rep(c(1,2),each=n/2) z <- rnorm(n, c(170,180)[sex], c(10,15)[sex]) ... 3 The reason one would use an OP is to study a categorical variables that is ordered, but where the actual values reflect only a ranking. For example, take bond ratings. There's an underlying variable that is unobserved called creditworthiness that some agency has divided into bins, which range from AAA, AA, A, BBB, and so on to D. You can imagine coding these ... 3 In this article \sigma is any function which maps an individual's score, which can typically be any number along (- \infty, \infty), to the interval (0, 1). The most commonly-used function is the sigmoid (the inverse logit) which looks like$$ \frac{e^{\beta^T x}}{e^{\beta^T x} + 1}$$and this is mentioned in the article. The function$\sigma$... 3 That is not a robustness check because the ordinary linear model is guaranteed not to fit. It will yield probabilities estimates outside$[0,1]$. A better approach to checking the assumptions of an ordinal regression model are: First, relax the assumptions allowing for nonlinear effects using regression splines Then, check the equal slopes (parallelism) ... 2 This question is very broad--to the point of not being very answerable. You should probably take some statistics classes or read some textbooks, and get very clear on the basics. That said, here are a couple of very broad points: An ordinal regression model will be appropriate for your data. There are many questions loosely similar to yours already on ... 2 Results from an ordered logit/probit regression are always unintuitive, but categorical explanatory variables are as meaningful as continuous ones. I'd even say that they are easier to interpret. For a concrete example, you could look at Dobson, An Introduction to Generalizer Linear Models, 2002, 2nd ed., Chapter 8. In her "car preferences" example, the ... 2 Have you looked into the stats literature on reduced-rank vector generalized linear models? It seems you might be trying to identify the model by introducing constraints that in effect make it a hybrid of the probit and ordinal regressions, plus with a multilevel structure on the right-hand side of the equation. This document (pdf alert) on the VGAM package ... 2 An ordinal regression model has multiple intercepts describing the baseline frequency of each outcome. In your case, you only had values 0, 2, and 4, so you have two intercepts denoted 0|2 and 2|4. So your question about the variance of the intercept cannot be interpreted unless you tell the which intercept are you talking about. So element$(1,1)$is the ... 2 That syntax won't work, and you will have received a warning that that constrained was ignored after your oprobit command. Instead you can add L2_individual as an explanatory variable, constrain the coefficient for that variable to be -1 and constrain the second cut value to be 0. 2 You only get one coefficient in an ordinal probit model because you are actually fitting the model for a latent continuous variable y* (rather than, say, the log-odds of each alternative relative to the base alternative in a multinomial logit model). Think about it this way: The ordinal variable categories are rankings, such that although your outcomes may ... 2 The R rms package has many capabilities for validating ordinal regression models. Start with the orm function. Note that split-sample validation takes an extremely large sample size to work. You might be better off with bootstrap validate as implemented in the rms validate and calibrate functions. Measures of predictive accuracy for ordinal$Y$include ... 2 Whether using polr or the R rms package's lrm and orm functions, there is one cutpoint for every unique value of$Y$except for the first. This is automatic. Printed output of lrm and orm fit objects uses a notation that is a bit more clear. The intercepts are constrained to be in order automatically, and if you compute the correct individual ... 2 If you have enough data you can use an ordered logit model or an ordered probit model. The difference between the two is the IIA assumption. Here is a good description of the IIA to assumption and the difference between multinomial logit and multinomial probit. The difference between ordered logit and ordered probit can be described analogously. So, why ... 2 (I created a solution to the problem myself, so I give it as an answer here for anyone who is interested.) Method First, we have the data that we wish to estimate group differences from. These indicate the proportions of women and men, respectively, that exceed a certain threshold. For example, when$66.36\%$of women are taller than some threshold, then$...

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There is no problem with the code, the marginal effect is not bounded between 0 and 1, or -1 and 1. The marginal effect measures the slope of the probability at a particular point. For an example that illustrates that the marginal effect is unbounded, suppose we have a continuous variable that perfectly predicts the outcome, so if x>0.5 then the outcome is ...

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I'm a little bit confused by your use of "pairwise comparisons" to refer to a nested model comparison using the likelihood ratio test. The likelihood ratio is testing to see if: (a) the variance of the slopes is greater than zero, or (b) the covariance between the random slopes and intercepts is different from zero. I would first adjust your p-value for ...

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Generally your are estimating probabilities for every category j of your dependent variable y. Similar to marginal effects, not as far as I know. You can estimate the probabilites for the response-categories with mfx in stata if I remember correctly. Concerning the interpretation of the coefficients UCLA can help: "Standard interpretation of the ordered ...

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That looks correct; note that after you make the myData data frame, you can use: myData$y = factor(myData$y) reg <- polr(y ~ x, data = myData, method = "probit") Later, you can make the validation data with: myValidationData <- data.frame(x = c(5.6, 5.1), y = c(3,3)) Your syntax works fine, I just thought this was a bit "cleaner". Here's a great ...

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You need to use the i. prefix in front of connectivity to let Stata know that it is dealing with a categorical variable. Otherwise Stata will assume that it is continuous, which is why you only get one parameter. Some people do treat Likert scale variables as if they were continuous, but I would avoid it since it bakes in some strong assumptions. You can use ...

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(Partially answered in comments, summarized below) Like in about any kind of regression model, you can use any kind of variables as predictors. Categorical variables cannot be used directly, they must be encoded, but you can do that in exactly the same way you use for linear regression. So just go ahead!

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For simulation you use the predicted probabilities of belonging to each category. You draw a single column vector from a standard continuous uniform distribution, and assign a an observation to the first category if the random number is less than the first predicted probability, to the second catogry if it is larger than the first predicted probability but ...

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If the name of your model object is fit, predict(fit, type = 'class') will return the predicted class for the data you fit your model to. If you simulate data, (however you like), you can pass this to the predict function via the newdata argument, and get predicted categories or probabilities, whichever you prefer. expand.grid is great for doing that also. ...

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