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I am trying to use a regression model which can predict the category of an object.One object has many variables (these are used in the model as independent variables). My question is what kind of regression model does one need in order to get a categorical variable as a dependent variable.

I'm basically trying to classify object using a regression model. I don't quite know how this works when the response variable is a categorical variable.

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A logistic regression can accommodate binary dependent variables and a multinomial logistic regression can accommodate ordinal dependent variables with more than two levels.

For a discussion on the comparisons between the two see also here.

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In the machine learning terminology you are refererring to a classification problem and not to a regression problem. The difference being that in classification problems the response (dependent) variable is discrete while in regression problems your response variable is continuous.

Having said this, you may convert a regression problem into a classification problem as follows. Map your continuous response (obtained from a regression problem) into the [0,1] inteval, by means of a suitable transformation, such as the logistic function. In the binary case, classification is then done by means of a sgn(x-0.5) function, where x is the transformed continuous response obtained from the regression model. In a multiple categories classification setting, you may perform one binary regression model for each category and choose the category with the highest response.

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