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I am reviewing a number of research papers regarding domestic space heating energy consumption which used multiple regression techniques to identify the main determinants of space heating in the diverse (heterogeneous) types of homes that exist in north-western Europe.

The predictors are categorised into three groupings: building physics inputs (e.g. total floor area, age of building, insulation levels, whether double glazed or not, etc), socio-demographic inputs (age of occupants, household income, employment status) and heating behaviour inputs (proportion of rooms heated, heating hours per day, regular or irregular heating patterns).

In all research papers, all of the three categories' inputs were "lumped in" together (excuse my ignorance) to produce coefficients for all of the predictors, and a coefficient of multiple determination (plus an adjusted R-squared to account for sample size and the number of predictors). After admitting all of the predictors into the model, each researcher proceeded to analyse each grouping separately, but always in the same order: first by introducing the building physics predictors, then by adding the socio-demographic predictors, and finally by adding behavioural predictors, with the hindsight that the building physics predictors are always the most dominant.

My question is: would it change the significance or the relative importance [beta values in most, but not all papers])of the predictors if, say, the behavioural factors were introduced first into the regression model, followed by the socio-demograhic factors and then followed by the building physics factors?

Each of the three groupings has around 10 predictors in each.

Collinearity becomes a problem when each further grouping is introduced (such as between higher income and larger house size), which sometimes results in the exclusion of (what I think is) a highly significant determinant (such as income, which is "over-shadowed" by house size). Actually, only one paper (published in 2015) excluded "income" using a Lasso regression technique.

I am aware of high VIF's (>5 or >10, depending on source reference) being used to identify collinearity, which would encourage exclusion of a predictor.

To re-iterate: does it matter in which order that predictors are introduced into a (any) multiple regression technique?

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  • $\begingroup$ Welcome to our site! I think this is a near-duplicate of Does the order of explanatory variables matter when calculating their regression coefficients? although you are obviously approaching from a slightly different angle, and that question has much more focus on the technical "why", whereas your question avoids the underlying mathematics. $\endgroup$ – Silverfish Jun 17 '16 at 23:53
  • $\begingroup$ @silverfish. The link is far beyond my comprehension of statistical analysis. Apologies if my query is not as specific as the site requires. I was hoping it may be a Yes/No answer. $\endgroup$ – ghunter Jun 18 '16 at 0:20
  • $\begingroup$ @ghunter answer is Yes. $\endgroup$ – SmallChess Jun 18 '16 at 3:57
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I think the answer may be fairly simple. Let's say you have 10 physical variables and 10 demographic variables. And, you can include all 20 variables in your model without running into any multicollinearity issues and statistical significance issues (all variables are statistically significant). In such a situation, the order of your variables make no difference since you are able to include them all. However, such a situation may be highly unlikely.

You are more likely to run into issues of statistical significance and multicollinearity. Those issues will force you to remove or not select some of the variables of either types. And, in such a situation the order will have a material impact on not only the selected variables in the model, but also both their regression coefficient and standardized coefficient. In other words, the order affects everything the minute you deal with a model that does not include all the variables or that you compare similar model that do not have an identical variable selection. But, if your model includes all 20 just fine, whether you start selecting them from 1 to 20 or 20 to 1 makes no difference.

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  • $\begingroup$ Could you possibly re-phrase your answer? Re: "the order will have a material impact on not only the selected variables in the model..". I understand that the remaining predictors will have different coefficients when insignificant variables are excluded from the RA, and the RA is run again, but are you saying that the original order of the placement of predictors into the RA will affect the coefficients of the predictors, i.e. you place the most significant predictor (from prior knowledge) first, into the RA? I hope I have mis-read your reply.. $\endgroup$ – ghunter Jun 18 '16 at 3:21
  • $\begingroup$ What do you mean by RA? $\endgroup$ – Sympa Jun 18 '16 at 3:23
  • $\begingroup$ Regression analysis, sorry. $\endgroup$ – ghunter Jun 18 '16 at 3:24
  • $\begingroup$ Let's say you have a model with 5 variables that I simply call 1, 2, 3, 4, and 5. In the first situation, all five variables make the cut, are statistically significant, and are not multicollinear. No problem. It does not matter whether you start by including them starting from 1 or starting from 5. In second situation, variable 1 and 5 are multicollinear to each other. In that case, it makes a lot of difference in what order you start selecting them. You end up with different variables and coefficients. $\endgroup$ – Sympa Jun 18 '16 at 3:43
  • $\begingroup$ Apologies, Sympa. I will have to completely re-write my original question, having re-read the research papers. I have three groups of predictors (Group1: 1,2,3,4,5), (Group 2: a,b,c,d,e) and (Group 3: p,q,r,s,t). An ordinary least squares regression (OLS) was run on each group separately (within each group, VIFs were identified and certain predictors excluded). Group 1 was then combined with Group 2. Sorry, will have to re-write original Q tomorrow: running out of space here. $\endgroup$ – ghunter Jun 18 '16 at 4:50

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