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I have two IVs that are highly correlated with each other at 0.979 (Pearson) & 0.919 (Kendall's).

IV1: Quality of response
IV2: Quality of Technical Advice

Sample Size: 252

Considering the similarity in the phrasing of the IVs, could it mean that the respondents do not perceive a difference between the two measurements?

Would it be appropriate to drop one of the items?

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    $\begingroup$ Instead of dropping one of the items, you could replace one of the two by their difference. The resulting variables are usually only weakly correlated and (in contrast e.g. to principal components) easy to interprete. $\endgroup$ – Michael M Aug 29 '14 at 14:00
  • $\begingroup$ Thanks Michael! So you mean replacing for instance IV2 with IV1-IV2? $\endgroup$ – GentlemanEddie Aug 29 '14 at 14:32
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    $\begingroup$ Exactly. Or by IV2 - IV1, depending on your preferences. Things like this should generally be decided without taking correlations with the DV into account (i.e. not as James suggests) to avoid overfitting. $\endgroup$ – Michael M Aug 29 '14 at 14:39
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    $\begingroup$ 1) One can't know if there is overfitting before any fitting was done. This is related to one of weaknesses of PCA: when it selects the "derived inputs", the response is not taken into account at all. $\endgroup$ – James Aug 29 '14 at 14:52
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    $\begingroup$ 2) Taking a difference may be a good idea, assuming that IVs are on the same scale/comparable. $\endgroup$ – James Aug 29 '14 at 14:53
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You may end up dropping one or even both of them but first you need to fit the response and see what R-squared, AIC or other model selection tools tell you.

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  • $\begingroup$ Thanks James! R-Squared does not change much when I drop one of them (from 0.667 to 0.662), but drops more when I take them both out (down to 0.570). Not sure what this tells me though.. Help would be appreciated. $\endgroup$ – GentlemanEddie Aug 29 '14 at 14:43
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    $\begingroup$ What is the overall model p-value? $\endgroup$ – James Aug 29 '14 at 14:51
  • $\begingroup$ All models have been significant at 0.000 so far $\endgroup$ – GentlemanEddie Sep 1 '14 at 6:03
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    $\begingroup$ It looks like you just need to keep one of predictors (no matter which) unless you care for 0.5% gain in R-squared. $\endgroup$ – James Sep 2 '14 at 16:33

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