Numerical coding and constraints for categorical variables I know that using numerical coding is wrong but I'm trying to understand exactly why.
Suppose we want to fit the model $\text{prestige} = \beta_{0}+\beta_{1}\text{education}+\beta_{2}\text{type}+\epsilon$ and $\epsilon \sim N(\textbf{0},\sigma^{2}I_{n})$ where 'type' means occupation type.
If we were to encode for the categorical variable $\text{type}$ with three categories, blue collar, professional and white collar with 1, 2, and 3 respectively, we get 'unwanted assumptions/constraints' on the location of the intercepts.
Can someone please explain what is meant by this? 
 A: I think that encoding $type$ with the numbers $\{1,2,3 \}$ leads to three major problems: 
1) Giving a clear ranking between blue collar, professional and white collar automatically gives some pre-assumptions about the dependence structure in your model. Because if we have for example a $\beta_2>0$, then you assume that the effect of prestige for white collar must be stronger than for professional or white collar.
2) And more importantly it leads to the assumption that the difference between the three categories is equally spaced. I.e. you implicitly assume that the difference between blue collar and professional is the same as the difference between professional and white collar, while the difference between blue collar and white collar is twice the difference of them.
3) Somewhat related, but noteworthy, is that you also assume that $type$ is a real valued continuous variable what in fact is not true. 
Hence, the best solution would be to introduce three dummy variables $bc=I(blue collar=T)$, $pr=I(professional=T)$ and $wc=I(white collar=T)$, that are one if the statement in the indicator function $I(\cdot)$ is true. 
Then you leave out the constant and form a model like:
$$prestige=bc + pr + wc+\beta_1education+\epsilon,\epsilon∼N(0,\sigma^2I) $$
With this dummy specification you circumvent the problems 1)-3) as you do not need to assume a ranking, you also impose no spacing of the difference between the categories and additionally you code it binary instead of real valued.
