[R-sig-ME] Model building problem?
Luciano La Sala
lucianolasala at yahoo.com.ar
Sat Mar 13 23:07:56 CET 2010
Hello everyone,
I am building a model using the “lmer” function. I have IgG (continuous) as my outcome of interest, and the following variables as fixed effects: Egg Breadth (continuous), Egg Length (continuous), EggVolume (continuous), Clutch Size (three levels), and Hatching Order (three levels), plus random intercepts for NestID.
In model selection, terms were eliminated from a maximum model (with random intercept) to achieve a simpler model that retained only the significant main effects and interactions, using the Akaike information criterion.
At each step of model reduction, I look at the p-values of coefficients and decide which variable to eliminate next, re-fit the model and then I compare AIC values to decide whether the new model is a better fit for my data or not.
To my dismay, the best model is the one containing only the random intercept.
Stepwise variable elimination reduces AIC (see output) despite low p-values for the coefficients of the variables dropped! I would think that at least some of my variables (not just the random effect) should improve the model fit. It strikes me as very odd that the model with only random intercepts offers the best fit, being that random effect variances is close to zero (see output).
Q1. Should I stop simplifying my model at Step 2 or 3, where all main effects have p < 0.05?
Q2. However, AIC keeps dropping thereafter -regardless of significant p values of main effects- until no single main effect is left in the model. This baffles me!
Q3. Last but not least… where am I going so wrong here?
Thank you very much for whatever help you may give me!
Here goes a summary of the outputs:
FULL MODEL
Linear mixed model fit by REML
Formula: ELISA2~EggBreadth+EggLength+ClutchSize+HatchOrder+ EggVolume+(1|NestID)
AIC BIC logLik deviance REMLdev
-544.1 -511.6 282.1 -632.2 -564.1
Random effects:
Groups Name Variance Std.Dev.
NestID (Intercept) 0.00016440 0.012822
Residual 0.00207281 0.045528
Number of obs: 191, groups: NestID, 111
Fixed effects:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 3.545249 2.268083 1.563 0.1198
EggBreadth -0.066974 0.046930 -1.427 0.1553
EggLength -0.017986 0.016281 -1.105 0.2707
ClutchSizeTwo-eggs 0.009885 0.011652 0.848 0.3974
ClutchSizeThree-eggs -0.014039 0.011518 -1.219 0.2245
HatchOrderSecond 0.015605 0.008245 1.893 0.0600
HatchOrderThird 0.032599 0.011763 2.771 0.0062
EggVolume 0.019498 0.014616 1.334 0.1839
BACKWARD 1. Drop Clutch Size
Linear mixed model fit by REML
Formula: ELISA2~EggBreadth+EggLength+HatchOrder+EggVolume+(1|NestID)
AIC BIC logLik deviance REMLdev
-556.4 -530.4 286.2 -625.6 -572.4
Random effects:
Groups Name Variance Std.Dev.
NestID (Intercept) 0.00017555 0.013250
Residual 0.00211661 0.046007
Number of obs: 191, groups: NestID, 111
Fixed effects:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 3.089050 2.281486 1.354 0.1774
EggBreadth -0.057337 0.047197 -1.215 0.2260
EggLength -0.013941 0.016351 -0.853 0.3950
HatchOrderSecond 0.014215 0.007875 1.805 0.0727
HatchOrderThird 0.021879 0.010740 2.037 0.0431
EggVolume 0.015693 0.014661 1.070 0.2858
BACKWARD 2. Drop EggLength
Linear mixed model fit by REML
Formula: ELISA2 ~ EggBreadth + HatchOrder + EggVolume + (1 | NestID)
Formula: ELISA2 ~ EggBreadth + HatchOrder + EggVolume + (1 | NestID)
AIC BIC logLik deviance REMLdev
-564.1 -541.3 289.1 -624.8 -578.1
Random effects:
Groups Name Variance Std.Dev.
NestID (Intercept) 0.00015766 0.012556
Residual 0.00212966 0.046148
Number of obs: 191, groups: NestID, 111
Fixed effects:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 1.148186 0.148751 7.719 0.0000
EggBreadth -0.017284 0.004517 -3.826 0.0002
HatchOrderSecond 0.014918 0.007848 1.901 0.0588
HatchOrderThird 0.022059 0.010734 2.055 0.0413
EggVolume 0.003230 0.001148 2.813 0.0054
BACKWARD 3. Drop EggBreadth
Linear mixed model fit by REML
Formula: ELISA2 ~ EggLength + HatchOrder + EggVolume + (1 | NestID)
AIC BIC logLik deviance REMLdev
-561.2 -538.5 287.6 -624.1 -575.2
Random effects:
Groups Name Variance Std.Dev.
NestID (Intercept) 0.00015423 0.012419
Residual 0.00214197 0.046281
Number of obs: 191, groups: NestID, 111
Fixed effects:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.3196987 0.0912062 3.505 0.0006
EggLength 0.0058330 0.0015671 3.722 0.0003
HatchOrderSecond 0.0149907 0.0078835 1.902 0.0588
HatchOrderThird 0.0219364 0.0107628 2.038 0.0429
EggVolume -0.0020977 0.0007405 -2.833 0.0051
BACKWARD 4. Drop HatchOrder
Formula: ELISA2 ~ EggBreadth + EggVolume + (1 | NestID)
Linear mixed model fit by REML
AIC BIC logLik deviance REMLdev
-577.4 -561.1 293.7 -618.9 -587.4
Random effects:
Groups Name Variance Std.Dev.
NestID (Intercept) 0.00010214 0.010106
Residual 0.00222943 0.047217
Number of obs: 191, groups: NestID, 111
Fixed effects:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 1.084503 0.146243 7.416 0.0000
EggBreadth -0.014484 0.004371 -3.314 0.0011
EggVolume 0.002409 0.001099 2.193 0.0295
BACKWARD 5. Drop EggVolume
Formula: ELISA2 ~ EggBreadth + (1 | NestID)
Linear mixed model fit by REML
AIC BIC logLik deviance REMLdev
-586.5 -573.5 297.2 -614.1 -594.5
Random effects:
Groups Name Variance Std.Dev.
NestID (Intercept) 0.00017172 0.013104
Residual 0.00221031 0.047014
Number of obs: 191, groups: NestID, 111
Fixed effects:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.884482 0.115833 7.636 0.0000
EggBreadth -0.006443 0.002401 -2.683 0.0079
BACKWARD 6. Drop Egg Breadth
Formula: ELISA2 ~ 1 + (1|NestID)
Linear mixed model fit by REML
AIC BIC logLik deviance REMLdev
-591.6 -581.8 298.8 -607 -597.6
Random effects:
Groups Name Variance Std.Dev.
NestID (Intercept) 0.0001917 0.013846
Residual 0.0022692 0.047636
Number of obs: 191, groups: NestID, 111
Fixed effects:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.573809 0.003727 153.9 0
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