I am curious why the two versions of my regression model in R give different results for the quadratic term. If I have understood correctly, using the function poly(x,2,raw=TRUE) should give the same result as the use of raw polynomials based on I(x^2). What could be the reason that this is not the case for me?
The models:
remltf <- FALSE
summer_3_full_remlFALSE1 <- glmmTMB(case ~
sex. * I(tree.cover^2) +
sex. * DE.edge +
sex. * DI.crops.log +
sex. * DI.grass.log +
sex. * DI.settle.log+
sex. * DE.road +
sex. * DE.edge +
(1 | id),
family = binomial (link=logit), data = rsf.summer.3,
REML = remltf, control=glmmTMBControl(optimizer=optim, optArgs=list(method="BFGS")))
summer_3_full_remlFALSE <- glmmTMB(case ~
sex. * poly(tree.cover,2,raw=TRUE) +
sex. * DE.edge +
sex. * DI.crops.log +
sex. * DI.grass.log +
sex. * DI.settle.log+
sex. * DE.road +
sex. * DE.edge +
(1 | id),
family = binomial (link=logit), data = rsf.summer.3,
REML = remltf, control=glmmTMBControl(optimizer=optim, optArgs=list(method="BFGS")))
Model summaries:
> summary(summer_3_full_remlFALSE)
Family: binomial ( logit )
Formula: case ~ sex. * poly(tree.cover, 2, raw = TRUE) + sex. * DE.edge +
sex. * DI.crops.log + sex. * DI.grass.log + sex. * DI.settle.log +
sex. * DE.road + sex. * DE.edge + (1 | id)
Data: rsf.summer.3
AIC BIC logLik deviance df.resid
111952.8 112125.2 -55959.4 111918.8 187588
Random effects:
Conditional model:
Groups Name Variance Std.Dev.
id (Intercept) 0.01662 0.1289
Number of obs: 187605, groups: id, 55
Conditional model:
Estimate Std. Error z value Pr(>|z|)
(Intercept) -1.79198 0.03501 -51.18 < 2e-16 ***
sex.1 -0.02543 0.05028 -0.51 0.61308
poly(tree.cover, 2, raw = TRUE)1 -0.53122 0.02475 -21.47 < 2e-16 ***
poly(tree.cover, 2, raw = TRUE)2 -0.61447 0.02233 -27.51 < 2e-16 ***
DE.edge 0.07675 0.01252 6.13 8.80e-10 ***
DI.crops.log -0.11048 0.01593 -6.94 4.02e-12 ***
DI.grass.log -0.11473 0.01535 -7.47 7.90e-14 ***
DI.settle.log 0.16486 0.01437 11.47 < 2e-16 ***
DE.road -0.13558 0.01267 -10.71 < 2e-16 ***
sex.1:poly(tree.cover, 2, raw = TRUE)1 0.10300 0.03288 3.13 0.00173 **
sex.1:poly(tree.cover, 2, raw = TRUE)2 0.01762 0.03278 0.54 0.59082
sex.1:DE.edge -0.03911 0.02009 -1.95 0.05158 .
sex.1:DI.crops.log 0.11371 0.02906 3.91 9.14e-05 ***
sex.1:DI.grass.log 0.35854 0.02632 13.62 < 2e-16 ***
sex.1:DI.settle.log -0.05411 0.02225 -2.43 0.01501 *
sex.1:DE.road 0.13399 0.01932 6.94 4.05e-12 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
> summary(summer_3_full_remlFALSE1)
Family: binomial ( logit )
Formula: case ~ sex. * I(tree.cover^2) + sex. * DE.edge + sex. * DI.crops.log +
sex. * DI.grass.log + sex. * DI.settle.log + sex. * DE.road +
sex. * DE.edge + (1 | id)
Data: rsf.summer.3
AIC BIC logLik deviance df.resid
112793.3 112945.4 -56381.7 112763.3 187590
Random effects:
Conditional model:
Groups Name Variance Std.Dev.
id (Intercept) 0.0112 0.1058
Number of obs: 187605, groups: id, 55
Conditional model:
Estimate Std. Error z value Pr(>|z|)
(Intercept) -2.05515 0.03013 -68.22 < 2e-16 ***
sex.1 0.04656 0.04405 1.06 0.29050
I(tree.cover^2) -0.31710 0.01804 -17.58 < 2e-16 ***
DE.edge 0.09860 0.01251 7.88 3.25e-15 ***
DI.crops.log -0.23889 0.01508 -15.84 < 2e-16 ***
DI.grass.log -0.28127 0.01365 -20.61 < 2e-16 ***
DI.settle.log 0.12951 0.01426 9.08 < 2e-16 ***
DE.road -0.13119 0.01268 -10.34 < 2e-16 ***
sex.1:I(tree.cover^2) -0.09153 0.02931 -3.12 0.00179 **
sex.1:DE.edge -0.01384 0.01984 -0.70 0.48546
sex.1:DI.crops.log 0.13521 0.02782 4.86 1.17e-06 ***
sex.1:DI.grass.log 0.38901 0.02480 15.69 < 2e-16 ***
sex.1:DI.settle.log -0.03838 0.02201 -1.74 0.08117 .
sex.1:DE.road 0.12036 0.01933 6.23 4.75e-10 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
>
Thanks in advance