 In this video, I will demonstrate the no-perfect-colonarity assumption of Richardson analysis. The perfect-colonarity assumption means that each independent variable must bring unique information to the model. So it cannot be possible to infer values for one independent variable based on other independent variables. Let's see what that means. Here is the data for the prestige dataset and we have a categorical variable type. If we create dummy variables for the categorical variable type, we know that if the type blue color or type professional are both zero, then the observation must be type white color. On the other hand, if type blue color or type professional is either one of them is one, then type white color must be zero. So the type white color doesn't give us any new information if we know the type blue color and type professional. In practice, when we do a Richardson analysis where we specify the type as a categorical variable, we will get two estimates. We will get the estimate of type professional and type white color and one of these categories is left out as a reference category. The reason for leaving it out is that including it in the model leads to violation of no perfect-colonarity assumptions. So let's try and see what happens when we force all three dummies to be included in the model. So I have to specify the dummies manually and then specify them into the model manually. So I specified a model like that. We have type blue color, type white color, type professional here and we try to estimate the model. We get a warning that one defined because of singularities. So that warning tells us that we are in violation of the no perfect-colonarity assumption and in the results we will see that one of these variables was dropped in the analysis. So the estimate of type professional couldn't be or the effect couldn't be estimated. And this is a very common behavior. You cannot estimate the Richardson model that includes all these three dummies because of perfect-colonarity. It's mathematically impossible. So the software has two alternatives. Either it refuses to even try or it just drops one of the variables to make them all estimable. Whichever variable is dropped probably depends on the order of entry of the variables but it's not documented behavior of R. So when you see that you don't get estimates for some of the variables, that is a pretty good indication that you are in violation of the no perfect-colonarity assumption and you need to do something about your model or it could also be an indication that you have done a data coding mistake or data preparation mistake accidentally copied for example one variable to your data set twice under different names. So that can happen as well. When you encounter these no estimates or NAs or periods depending on the statistical software it indicates a data problem.