I have some difficulty assessing the level of measurement of these two variables...

When time spent reading a book has been measured with the categories 0 (=never), 0.5 (about 1 hour), 1.5 (about 2 hours), 2.5 (about 2 - 3 hours), 3.5 (more than 3 hours). I would say this is an ordinal / categorical measure, due the unequal differences in values!

The second variable is number of close friends: 0, 1, 2 or 3 (which indicates 3 or more). I would say this is also an example of a categorical measure!

Is it allowed to use the first variable as independent variable in a regression analysis?

Is it allowed to use the second variable as dependent variable in a regression analysis

  • $\begingroup$ And what would the correct analysis be, a categorical analysis right? $\endgroup$ – NathanD Oct 3 '17 at 12:25
  • 3
    $\begingroup$ You can use ordered categorical variables in both situations but you do need to deal with each appropriately. You might gain more insight from the threads tagged ordered-logit and ordinal-data on this site. $\endgroup$ – mdewey Oct 3 '17 at 12:42
  • $\begingroup$ The notion of "which test is allowed" should be expunged from textbooks; Stevens' paper has some good points and some problematic issues -- &that's fine -- but what people have done with it since is a disaster - quite counterproductive to reasonable practice. Instead students should be learning how to start with a hypothesis that relates to their variables and learn how to work out how to test hypotheses that actually matter to them. Otherwise you end up nonsensically applying location tests when you're interested in spread because that's what's "allowed" according to some silly list. $\endgroup$ – Glen_b Oct 3 '17 at 23:12

As to the first two remarks: 'time spent reading a book' would indeed be categorical. In this case, your reasoning is fine. There are unequal and vague differences between the values which means the scale is not continuous. It is rather a set of ordered categories. Moreover, the number of different values is small (only 4 possible values), making it hard to say whether this variable could actually be modeled as continuous (whether its data generating mechanism is or not).

The same goes for the number of close friends.

For the third question/point see Regression for categorical independent variables and a continuous dependent one. In short, for a general regression model the kind of independent variables (continuous or categorical) does not matter (i.e. it can be both), but note that the categorical data needs to be dummy-recoded for some software applications.

As to your last question, the type of dependent variable does matter. A linear regression will violate most, if not all, of its assumptions when used to study a binary dependent variable. Luckily for us, this is easily overcome by using 'generalized linear models'. A couple of examples: for binary outcomes this means you use logistic regression; for count data you use Poisson regression; and for categorical data with more than two levels you use multinomial regression when the dependent variable is not ordered, and ordinal regression when the dependent variable has more than two levels and is ordered. I feel the latter might apply to your situation.

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