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I want to run geographically weighted regression (GWR) with 5 independent variables (the first one is of my direct interest, while four are confounders). I ran various models (with fixed bandwidth [BW]) and for and each, I received AICc and AIC. Following is the output:

       [BW]   [AICc]     [AIC]
 [1,]   92 -1219.667 -1160.555     
 [2,]   92 -1223.569 -1166.525
 [3,]   92 -1231.206 -1175.681   
 [4,]   92 -1234.278 -1177.220
 [5,]   92 -1253.736 -1200.312
 [6,]   92 -1262.010 -1208.239
 [7,]   92 -1297.094 -1212.467 
 [8,]   92 -1297.599 -1219.058 
 [9,]   92 -1303.253 -1220.423
[10,]   92 -1305.397 -1223.153 
[11,]   92 -1318.119 -1237.963 
[12,]   92 -1342.503 -1235.855 
[13,]   92 -1344.737 -1235.568 
[14,]   92 -1356.322 -1243.391 
[15,]   92 -1367.295 -1256.171 
[16,]   92 -1387.675 -1242.861 
[17,]   92 -1389.274 -1247.099 
[18,]   92 -1395.720 -1255.762 
[19,]   92 -1416.640 -1243.229 
[20,]   92 -1417.227 -1241.243
[21,]   92 -1440.021 -1227.826 

My question is, should I consider AIC or AICc to choose the better model? As you can see, smallest AICc corresponds to model # 21 and smallest AIC corresponds with model # 15 & 18. This is bothering me because model # 21 has all five variables, while model 15 has only three confounders (out of 4) and model 18 has all the confounders. In both of these last two models, I do not have main predictor variable.

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    $\begingroup$ Welcome to CV. Since you’re new here, you may want to take our tour, which has information for new users. What does GWR stand for? $\endgroup$ – T.E.G. - Reinstate Monica Aug 18 '17 at 20:38
  • $\begingroup$ Thanks. GWR stands for geographically weighted regression. $\endgroup$ – Owais Raza Aug 18 '17 at 20:41
  • $\begingroup$ @OwaisRaza Edit your explanation of "GWR" into your question rather than writing it as a comment. $\endgroup$ – Kodiologist Aug 18 '17 at 23:43
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According to the Wikipedia entry for AICc, Burnham & Anderson (2002, ch. 7) recommend not to use AIC without the bias correction term (i.e. do not use AIC) unless

$$\frac{N}{K} < 40$$

where $K$ is the total number of parameters of the likelihood and $N$ is the sample size but this is not set in stone. You should check if that makes sense for your specific problem.

It's on page 445 of their book:

Model Selection and Multimodel Inference: A Practical Information-Theoretic Approach, Second Edition

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  • $\begingroup$ Yes, I am aware of this. Sample size in this study is 885. $\endgroup$ – Owais Raza Aug 18 '17 at 20:50

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