Create composite variables using items with different scales- dealing with multicollinearity I have IV's that are highly correlated with one another. The first set of correlated IV's, I combined them by adding the score and dividing by 2 to create a composite score. This was simple because both were on a scale 0-7. The other set, however, have different scales. One is measured on range 0-62, and the other 0-1. I want to combine these two to form a composite variable, as they measure the same concept. However, I really am not sure how. I want to use the variables to do a regression. Any help would be appreciated!!
 A: One way of doing it is by creating a variable $c =  a/(2 \times 62) + b/(2 \times 1) \in [0;1]$, where $a$ is the variable in the 0 to 62 scale and $b$ is the variable in the 0 to 1 scale. Therefore, $c$ would be the average of the normalized values of $a$ and $b$ (here the term "normalize" is not intended to mean the Gaussian distribution). The value of $c$ is close to $0$ if both $a$ and $b$ are close to zero and $c$ would be close to $1$ if both $a$ and $b$ are close to maximum of their respective scale.
Alternatively, you could create a variable that is the mean of the standardization of the other variables:
$$z = \frac{a-\bar{a}}{2s_a} + \frac{b-\bar{b}}{2s_b} ,$$
where $\bar{a}$ is the (sample) mean of $a$ and $s_a$ is the (sample) standard deviation of $a$ (and the same for $b$). This way, $z$ would have a mean of 0 and a variance of 1.
By the way, if you want another variable from $a$ and $b$ that has a low correlation with $z$, you could use the difference between the standardization of the variables:
$$w = \frac{a-\bar{a}}{s_a} - \frac{b-\bar{b}}{s_b} .$$
