Adding random error to ordinal IV to make it more continous

#1
In survey data, attududinal questions are often coded 1-5, 1-7, 0-10 etc.

These kinds of variables are often reffered to as approximately continous. They only have 5-10 unique values, but one can assume that there is an continuous underlying scale.

The limited number of uniqe data points make it difficult to assess some of the assumptions regarding normally distributed residuals and absense of heteroscedasticity. Scatterplots are also more difficult to interpret since a hundre observations can occupy the same point.

Why not recode the variable by adding a random value from a normal distribution with, say a mean of 0 and a SD of 0.5?

This will smoothen the distribution considerably, and allow for much more illustrative scatterplots and histograms.

Combining this method with logaritmic transforations, I have changed a severly left skewed variable (almost logaritmic in its distribution) with seriously skewed regression residuals, into an almost normally distributed variabel with almost perfectly normally distributed residuals.

This does not change the regression much, but one variable is only significant when using the "randomness-induced" and transformed independent variable.

So far I am just experimenting for fun, but are there any serious mathematical (or methodological) problems to increasing the variance slightly and making the independent variabel more continous in this way?
 

noetsi

Fortran must die
#2
Because the distrution you create won't reflect the distribution you are interested in? You can always add levels to an ordinal variable, the question would then be if what you created really reflects the original variable you wanted to analyze.