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Ordinal (ordered) logistic regression model. Used to model an ordered response â for example, low, medium, or high. Might also be called the ordinal multinomial logit model. Ordinal logistic models take into account the ordered nature of the response, which can result in simple, more powerful models.
Among such general linear models is polynomial regression. In that case, the entries $j$th column of $X$ are the $(j-1)$th powers of those in second column. In these models, the least-squares estimate of $\beta$ is $\hat\beta= (X^TX)^{-1}X^T Y$. A generalized linear model is not a linear model. You have a link function.