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I have a question regarding a binary logistic regression.

Its about the plausibility of the influence of one independent variable.

I am analyzing the influence of the size of a farm on the use of the plough.

Here I am showing the average values of this describing variable (there are all in all six variables). In the analysis I take the logarithm of this variable.

group 1 (n=66): non-user of plough (average value of farm size 267 hectares; log of farm size=2,2; histogram below)

enter image description here

group 2 (n=181): user of plough (average value of farm size = 333 hectares; log farm size = 2,2; histogram below)

enter image description here

Edit: Regression results + collinearity diagnostics:

enter image description here

The results say, the larger the farm size, the more likely it is to belong to group 1. Although the farm size in this group is obviously much lower.

I can find no errors in the data, but I am surprised about this result.

Would You say that these results are an indication for misspecification or problems within the data?

I think taking the logarithm leads to an re-adjusting of the farm size variable. However,I dont like to make this process undone, because I am analyzing further three dependent variables with the same set of independent variables.

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    $\begingroup$ A plot of group vs. farm size would be very helpful. $\endgroup$ – Matthew Drury Aug 1 '16 at 16:05
  • $\begingroup$ The output from your logistic regression would also be helpful in addition to @MatthewDrury suggestion. $\endgroup$ – mdewey Aug 1 '16 at 17:45
  • $\begingroup$ Thanks for your responds. Do the plots already help? There is one outlier in the farm size variable of group 2, but deleting this observation doesn´t change the results $\endgroup$ – Ole Aug 1 '16 at 21:05
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    $\begingroup$ Remember that the coefficient for farm size is reported with the other predictors' values held constant. If there are correlations among your predictors, this type of result is possible. We will need to see more details of your complete model to provide more help. $\endgroup$ – EdM Aug 1 '16 at 21:56
  • $\begingroup$ I added the results. However, I tested the VIF values. And there is no need to worry. $\endgroup$ – Ole Aug 1 '16 at 22:07
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As others said its hard to interpret effect of one variable with others included. A model comparison approach may help. Also, you might consider standardizing your predictors. You might find that farm size is relatively weak, albeit in the 'wrong' direction. As well, if you have high inter correlations between features you can sometimes get these sorts of counterintuitive parameter estimates. Examination of the correlation matrix may help with that.

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  • $\begingroup$ Thanks! I added the Collinearity diagnostics. Can you identify any issues? $\endgroup$ – Ole Aug 3 '16 at 7:14
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There are two things at play here. First off, there are five other variables, many of which appear to have strong effect sizes. Since these variables aren't completely independent, a positive correlation does not necessarily imply a positive coefficient. Second, you should look at the average of the log farm sizes rather than the log of the average farm sizes if you want to see which group is bigger in the eyes of your regression model.

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  • $\begingroup$ Yes, and the average values of the logarithms look pretty similar $\endgroup$ – Ole Aug 3 '16 at 7:18

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