How can a 'linear models' be used to predict the level of a categorical variable from continuous numerical variables? I am a 1st year undergraduate psychology student currently doing some statistics exercises following a class. The statistics topics we have currently covered is still basic, including the various types of t-test, chi-squared tests, correlations, as well as 'simple' linear models such as linear regression, ANOVA and ANCOVA (we have been using R to do these analyses). One of the practice exercises (using a dataset given to us) says to use linear models to investigate how the continuous numerical variable A and the continuous numerical variable B predict the level of an ordinal categorical variable Y (Likert scale data). However, it was my understanding that for the types of simple linear models mentioned above, the response variable for the model (i.e. the one we are predicting) has to be an (approximately) continuous variable, whereas this question is asking us to construct models with an ordinal categorical response variable.
I am confused what the question is expecting us to do therefore, and am wondering if I am missing something. Is it the case that I can construct an ANOVA using variable Y to predict the level of A and B separately, and from this can somehow see whether A or B predicts Y? Or is there another approach - I saw online some people mention a multinomial logistic regression or ordinal logistic regression can be used to predict the level of a categorical response variable from numerical explanatory variables, although we have not touched on the use of such generalised linear models except for looking a bit at binary logistic regression, so would be surprised if this is what it is getting at.
Any guidance on whether I have misunderstood some concept or overlooked an appropriate approach would be much appreciated.
 A: You can use linear models for ordinal dependent variables. This requires slightly stricter assumptions than the more advanced ordinal response models, but you can still do it, in the same way you can perform a linear regression with a binary outcome variable. It may not be the most appropriate model and there may be other forms of models that yield more accurate predictions or a better fit to the data, but that doesn't mean the simpler models are wholly inappropriate.
If you are a first year psychology undergrad and are being asked to find the relationship between predictors and an outcome, you are being asked to use linear regression. Ordinal regression isn't even taught to most grad students in psychology (i.e., you can get a PhD in psychology and never learn about ordinal response models, even if you use ordinal dependent variables in your research); it is considered an advanced statistical method. If you are interested in learning about it, I recommend you do so, but you should start with logistic regression for binary responses first (and some psychology grad students don't even learn that!).
