Significance of B-splines components in mixed-effects logistic regression (glmer)
fortunes::fortune("should be done")
The ANOVA comparisons should be all you need. car::Anova() or drop1()
or afex::mixed() are all convenience functions for that. Since
parameters for splines are harder to interpret, you could just leave out
that part of the parameter table ...
The freakonometrics post you cite concludes:
So, it looks like having a lot of non significant components in a
spline regression is not a major issue. And reducing the degrees of freedom is clearly a bad option. Furthermore, stepwise throwing-away of terms is a recipe for messing up your inference (snooping/garden of forking paths). Your modeling approach looks fine; you *could* use gamm4 to get penalized regression splines, but again, it's better from an inferential/non-snooping point of view to pick a sensible model and stick with it unless it's obviously problematic. On a technical level, it's not clear whether the "discrepancy" (not really) between the summary() results and the anova() results is due to (1) the combined effect of a term with several components being significant even when the individual components are not; (2) the difference between Wald tests (used in summary) and likelihood-based tests (used in anova()). This could be disentangled, but IMO it's only worth it from a pedagogical/exploratory perspective. Ben Bolker
On 2018-09-21 10:54 AM, Anne Lerche wrote:
Good afternoon,
I have a problem with reporting significance of b-splines components in
a mixed-effects logistic regression fit in lme4 (caused by a reviewer's
comment on a paper). After several hours of searching the literature,
forums and the internet more generally, I have not found a solution and
therefore turn to the recipients of this mailing list for help. (My
questions are at the very end of the mail)
I am trying to model the change in the use of linguistic variable on the
basis of corpus data. My dataset contains the binary dependent variable
(DV, variant "a" or "b" being used), 2 random variables (RV1 and RV2,
both categorical) and three predictors (IV1=time, IV2=another numeric
variable, IV3=a categorical variable with 7 levels).
I wasn't sure if I should attach my (modified) dataset, so I'm trying to
produce an example. Unfortunately, it doesn't give the same results as
my original dataset.
library(lme4)
library(splines)
library(languageR)
df <- dative[dative$Modality == "spoken",]
df <- df[,c("RealizationOfRecipient", "Verb", "Speaker",
"LengthOfTheme", "SemanticClass")]
colnames(df) <- c("DV", "RV1", "RV2", "IV2", "IV3")
set.seed(130)
df$IV1 <- sample(1:13, 2360, replace = TRUE)
My final regression model looks like this (treatment contrast coding):
fin.mod <- glmer(DV~bs(IV1, knots=c(5,9),
degree=1)+IV2+IV3+(1|RV1)+(1|RV2),
???????????????? data=df, family=binomial)
summary(fin.mod, corr=FALSE)
where the effect of IV1 is modelled as a b-spline with 2 knots and a
degree of 1. Anova comparisons (of the original dataset) show that this
model performs significantly better than a) a model without IV1 modelled
as a b-spline (bs(IV1, knots=c(5,9), degree=1)), b) a model with IV1 as
a linear predictor (not using bs), c) a model with the df of the spline
specified instead of the knots (df=3), so that bs chooses knots
autonomously, and d) a model with only 2 df (bs(IV1, df=2, degree=1)). I
also ran comparisons with models with quadratic or cubis splines, and
still my final model performs significantly better.
The problem is that I am reporting this final model in a paper, and one
of the reviewers comments that I am reporting a non-significant effect
of IV1 because according to the coefficients table the variable does not
seem to have a significant effect (outlier correction does not make a
big difference):
Fixed effects:
????????????????????????????????????? Estimate Std. Error z value Pr(>|z|)
(Intercept)??????????????????????????? 0.52473??? 0.50759?? 1.034??? 0.301
bs(IV1, knots = c(5, 9), degree = 1)1 -0.93178??? 0.59162? -1.575??? 0.115
bs(IV1, knots = c(5, 9), degree = 1)2? 0.69287??? 0.43018?? 1.611??? 0.107
bs(IV1, knots = c(5, 9), degree = 1)3 -0.19389??? 0.61144? -0.317??? 0.751
IV2??????????????????????????????????? 0.47041??? 0.11615?? 4.050
5.12e-05 ***
IV3level2????????????????????????????? 0.30149??? 0.53837?? 0.560??? 0.575
IV3level3????????????????????????????? 0.15682??? 0.48760?? 0.322??? 0.748
IV3level4???????????????????????????? -0.89664??? 0.18656? -4.806
1.54e-06 ***
IV3level5???????????????????????????? -2.90305??? 0.68119? -4.262
2.03e-05 ***
IV3level6???????????????????????????? -0.32081??? 0.29438? -1.090??? 0.276
IV3level7???????????????????????????? -0.07038??? 0.87727? -0.080??? 0.936
(coefficients table of the sample dataset will differ)
I know that the results of anova comparisons and what the coefficients
table shows are two different things (as in the case of IV3 which also
significantly improves model quality when added to the regression even
if only few levels show significant contrasts).
My questions are:
How can I justify reporting my regression model when the regression
table shows only non-significant components for the b-spline term? (Is
it enough to point to the anova comparisons?)
Is is possible to keep only some components of the b-spline (as
suggested here for linear regression:
https://freakonometrics.hypotheses.org/47681)?
Is there a better way of modeling the data? I am not very familiar with
gamm4 or nlme, for example.
Any help is very much appreciated!
Thank you,
Anne