I am running a glm model in R, with a dataset with a large number of variables (around 25). I have checked for collinearity, and there is quite some between some of groups of variables, so I have run the tests both with all and with a selected number of variables.
I want to have an explanatory model for an outcome, possibly might progress to have a predictive model later on.
I also have a significant portion of NA's, so although I have 200 rows, I only get 90 observations.
Below is the model with least AIC, chosen with stepAIC. I have chosen a poisson GLM, since the outcome is bound from 0 to 96. Gamma GLM was not possible as I have a number of 0's.
MODEL INFO:
Observations: 90
Dependent Variable: postWOMACpain_6
Type: Linear regression
MODEL FIT:
χ²(8) = 166.64, p = 0.00
Pseudo-R² (Cragg-Uhler) = 0.29
Pseudo-R² (McFadden) = 0.07
AIC = 411.52, BIC = 436.51
Standard errors: MLE
---------------------------------------------------
Est. S.E. t val. p
-------------------- ------- ------ -------- ------
(Intercept) -1.66 1.07 -1.55 0.12
anaesthesia.FG 0.94 0.53 1.78 0.08
preWOMACpain 0.26 0.07 3.57 0.00
rs6746030TRUE -0.83 0.56 -1.48 0.14
rs11898284TRUE 1.33 0.57 2.34 0.02
rs533586TRUE -2.44 0.70 -3.48 0.00
rs2075572TRUE 1.04 0.64 1.63 0.11
rs609148TRUE 1.77 0.68 2.61 0.01
rs6985606TRUE 0.81 0.55 1.48 0.14
---------------------------------------------------
Estimated dispersion parameter = 5.04
My query would be:
If the AIC increases when I remove every variable with a p-value > 0.05 in a stepwise manner, then I will end up with only a couple of factors.
For instance, removing anaesthesia.FG, rs6746030, rs6985606 yields:
MODEL INFO:
Observations: 90
Dependent Variable: postWOMACpain_6
Type: Linear regression
MODEL FIT:
χ²(5) = 138.56, p = 0.00
Pseudo-R² (Cragg-Uhler) = 0.24
Pseudo-R² (McFadden) = 0.06
AIC = 411.50, BIC = 429.00
Standard errors: MLE
---------------------------------------------------
Est. S.E. t val. p
-------------------- ------- ------ -------- ------
(Intercept) -0.99 0.96 -1.03 0.31
preWOMACpain 0.26 0.07 3.52 0.00
rs11898284TRUE 1.54 0.55 2.79 0.01
rs533586TRUE -2.04 0.69 -2.97 0.00
rs2075572TRUE 1.10 0.65 1.71 0.09
rs609148TRUE 1.21 0.64 1.90 0.06
---------------------------------------------------
Estimated dispersion parameter = 5.2
down to:
MODEL INFO:
Observations: 90
Dependent Variable: postWOMACpain_6
Type: Linear regression
MODEL FIT:
χ²(2) = 90.72, p = 0.00
Pseudo-R² (Cragg-Uhler) = 0.16
Pseudo-R² (McFadden) = 0.04
AIC = 414.86, BIC = 424.86
Standard errors: MLE
---------------------------------------------------
Est. S.E. t val. p
-------------------- ------- ------ -------- ------
(Intercept) -0.32 0.73 -0.44 0.66
preWOMACpain 0.19 0.07 2.81 0.01
rs11898284TRUE 1.62 0.57 2.84 0.01
---------------------------------------------------
Estimated dispersion parameter = 5.57
which has a higher AIC, but all variables are all significant.
Your help is much appreciated. All courses I have done do not seem to address this issue, so am not sure how to tackle it properly.
Thanks