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I'm reading a paper on a study where a number of respondents received questions which they graded using a scale of 1-5. In the conclusion, the authors wrote that they "arrived at linear multiple regression models for the consolidated dependent variable N". What does that mean?

(Disclosure: I am not a student of mathematical stats, so please use layman's terms)

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    $\begingroup$ "arrived at" just means "decided to use". "consolidated dependent variable N" means they constructed the dependent variable (e.g. perhaps from several raters, each rating 1-5 -- impossible to say from what you wrote so far). "linear multiple regression" is a standard statistical technique; I'm not good enough to explain this in the characters I have left. $\endgroup$ – zbicyclist Dec 5 '11 at 17:12
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    $\begingroup$ +1 zbicyclist: Should make it an answer -- unless you're too new to be able to do that. Get full credit for a good answer. $\endgroup$ – Wayne Dec 5 '11 at 18:20
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I guess the answer to this question can be very complex but I'll try to give a general idea of how "arriving at a model" works:

You have your outcome (the dependent variable) that you want to correlate different variables to. The problem is that if you have 5 observations, let's say patient height, then if you have a couple of variables you might risk that by combining two-three different variables each patient will get a unique combination generating the "perfect model". This is basically the same as knowing each patients name and checking their height in their chart. This is what is known as overfitting and the general problem with multiple regression.

Usually you need some kind of restriction so that this doesn't occur. There are different approaches to address overfitting the basic idea is that when you look how much each variable contributes you also punish that value by adding that variable, AIC and BIC are common measures for this. I'm currently working my way through Frank Harrel's book on Regression Modeling Strategies that is a very nice in-depth description of different methods.

Another important part is to use already known confounders. If previous similar studies have shown that gender has a big impact in the new study should probably have at least tested that variable.

Back to your question:

...arrived at linear multiple regression models for the consolidated dependent variable N

I think the key is the part in the method where they describe what variables were tested for and what method they used for choosing the independent variables. By also testing the model against a different set of observations or performing bootstrap tests (you pick a random subsample from your studied sample) you can get an idea of the degree of overfitting. Having 1-5 answers can be analyzed as nominal or continuous variables where if you use nominal variables strongly affect degrees of freedom and increases the risk of overfitting.

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Translation: "We shoved this into the stats package we learned to use as undergrads and hit the button we were told to years ago in that case, and a window popped up saying 'linear multiple regression'. We then copied the best looking of the resulting numbers into this paper."

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    $\begingroup$ +1 A little cynical perhaps, but I'm sure many of us privately provide similar assessments when we encounter similarly vague statements in papers. $\endgroup$ – whuber Dec 5 '11 at 20:25
  • $\begingroup$ Not exactly an answer, but this made me smile (knowingly). $\endgroup$ – Gorkamorka Dec 5 '11 at 21:47
  • $\begingroup$ +1 But not just undergrads. Grad students, post-docs, and professors are just as guilty. $\endgroup$ – jkd Dec 7 '11 at 5:06

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