# Should I use raw scores or profile scores for variables in a regression model?

I'm trying to build a regression model to predict subjective memory reports based on the following predictors: objective memory test, illness perceptions, verbal fluency, and mood. I also want to control for age, years of education and IQ by putting them into the regression model too. However, there's a problem.

The objective memory memory test (The Rivermead Behavioural Memory Test) gives you both raw scores and profile scores for the various subscales. Some, but not all, of the profile scores are converted based on IQ and age.

Also, the IQ estimate (The Test of Premorbid Functioning) converts raw scores to an IQ estimate, either just with the raw score, or with the raw score AND demographic variables of age, gender and years of education. The IQ estimate that includes demographic information is far more accurate than without.

If I use profile scores (with demographics) then aren't I controlling for them twice?

Should I use raw scores or profile scores? And what, and how should I enter these into the regression model?

Sorry if the above doesn't make sense. I'm not sure I understand it myself. I'm really struggling to get my head around this! Thanks!

First, if you are just interested in prediction then you can use whichever predicts better. I would split the data into training and test data sets and then run a few models in the training data, figurbe out which predicts best, and test it in the test data and use those estimates for parameters etc.

But if you are really just interested in prediction there may be better methods than regression, but they can be kind of "black box".

If you are also interested in explanation, that is, you want your variable to be explicable to others and (perhaps) to illuminate something about how these variables work, then you have to think about what explanations would add to the knowledge base.

Finally, what do you mean by "far more accurate"?

• Hi Peter We're looking for an explanation rather than prediction. Specifically, we believe that mood and illness perceptions will account for more of the variance in subjective memory than objective memory will. The IQ estimate is in fact a measure of premorbid functioning based on the observation that, even in the presence of brain injury, certain skills are relatively spared. Studies have shown that given healthy adults an IQ test, and the test of premorbid function - correlations increase when age, gender, years of ed are taken into account. Jul 10 '13 at 20:33

On the IQ test: you have one score that gives raw scores, and another that is adjusted for, say, age. Assuming the adjustment makes sense, you can and probably should use the adjusted score.

Here's why: you know that IQ depends crucially on age, that's why you would ideally want to adjust for it. If you only had the raw scores, you could build an adjusted measure by yourself (assuming you have age of the subject). The easiest way to do this would be via interactions. A linear regression like $$MemRep_i=\beta_0+\beta_1 Age_i+\beta_2 RawIQ_i+\beta_3 Age_i\times RawIQ_i+e_i,$$ accounts for the fact that the influence of IQ on your dependent variable varies with age. For example, an estimate of $\beta_3=.2$ would mean that every increase in the product $Age*RawIQ$ increases your MemRep score by .2 (I don't know if the scaling makes sense, but you get the idea). This is not to be confused with the direct effect of age, which is estimated in $\beta_1$, or the direct effect of RawIQ ($\beta_2$). In the above specification, however, the interaction is constrained to be linear -- this is the simplest way to adjust, but may be very restrictive or simply wrong. I am guessing the adjusted IQ scores you have are more sophisticated and should therefore be used. Using the adjusted score then replaces the RawIQ and interaction above, i.e., you would estimate $$MemRep_i=\beta_0+\beta_1 Age_i+\beta_2 AdjIQ_i+e_i.$$ Clearly, this is more convenient (and probably more accurate) than building the adjusted score yourself, especially since you mention IQ does not only depend on age, but also schooling etc., for which you would have to add interactions as well. The one exception is if you think these linear interations produce a better adjusted IQ score than what you have.

The question whether you should use raw or adjusted score for your dependent variable is a different story. I would say the choice is mostly driven by your task: you want to predict the MemRep score - the adjusted one or the raw score? In particular, if you do not have access to adjusted scores later, then there is no point in building a model that predicts adjusted scores, and you should stick to the raw scores. As a side remark, if you estimate a model with adjusted MemRep score and do include predictors that have also been used in the adjustment, then you can actually see whether these predictors have predictive power left. If some predictor is significantly different from zero -- say age is positive -- that would mean the adjustment did not sufficiently account for age differences and with higher age of the subject you would predict a higher MemRep score.

Last remark: since you want to predict well, divide your data set randomly into training and validation data set. You estimate the parameters using only the training set, and then predict the MemRep scores for the validation sample. Do this with different speficiations (using raw scores, adjusted scores, with/without interactions etc.). Then just stick to what works best.

• Hi Nameless, thank you! Using adjusted scores would be ideal but then the demographics used (age, years of ed) would be controlled for multiple times and have an unduly large effect. By this I mean that I would control for IQ, age and years of ed, when IQ has already been calculated by controlling for age and years of ed. The other predictors (mood, verbal fluency, illness perceptions) don't account for demographics and so only some of my factors would be adjusted, and others not. I think I'll just have to bite the bullet and accept a less accurate estimate of IQ... Lesser of two evils... Jul 10 '13 at 20:36