[R-sig-ME] Main effects dilemma in logistic regression
Francesco Romano
|brom@no77 @end|ng |rom gm@||@com
Mon Aug 26 12:05:41 CEST 2019
Dear all,
Apologies for cross-posting if you are also part of R-ling-lang.
I am struggling to understand my results and would appreciate some advice
on a matter that has more to do with understanding logistic regression
outputs in R than actual issues with ME.
I have modelled a binomial mixed effects regression via glmer with two IVs,
a Task factor with two levels (AJT, priming) and a Proficiency continuous
predictor centered on its mean (proficiency). The DV is correct versus
incorrect response on the two tests. Participants and items are added as
random effects along with a slope of task by participants.
The main effects analysis of the model
*correctness ~ task * cent_Proficiency + (1 + task | Participant) + (1 |
item)*
is as follows
> car::Anova(profmodL2)
Analysis of Deviance Table (Type II Wald chisquare tests)
Response: correctness
Chisq Df Pr(>Chisq)
task 17.1340 1 3.483e-05 ***
cent_Proficiency 0.2377 1 0.625868
task:cent_Proficiency 7.6260 1 0.005753 **
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
What I am interested in is the relationship between the continuous
predictor and each level of task. As far as I understand, the main
interaction here is irrelevant to my query since what I am really after is
understanding is whether each increase in unit for proficiency results in
statistically significant log odd increase or decrease on each task. Thus,
I investigating simple effects of proficiency at each of the two levels of
the task factor.
Simple effect analysis yields:
> summary(profmodL2)
Cov prior : item ~ wishart(df = 3.5, scale = Inf, posterior.scale = cov,
common.scale = TRUE)
: Participant ~ wishart(df = 4.5, scale = Inf, posterior.scale =
cov, common.scale = TRUE)
Prior dev : 2.2697
Generalized linear mixed model fit by maximum likelihood (Laplace
Approximation) [bglmerMod]
Family: binomial ( logit )
Formula:
correctness ~ task * cent_Proficiency + (1 + task | Participant) +
(1 | item)
Data: prodataL2
Control: glmerControl(optimizer = "bobyqa")
AIC BIC logLik deviance df.resid
1288.2 1331.0 -636.1 1272.2 1547
Scaled residuals:
Min 1Q Median 3Q Max
-1.6314 -0.4378 -0.2570 -0.1624 4.8020
Random effects:
Groups Name Variance Std.Dev. Corr
item (Intercept) 1.0547 1.0270
Participant (Intercept) 0.5403 0.7350
taskpriming 0.7617 0.8728 -0.70
Number of obs: 1555, groups: item, 219; Participant, 13
Fixed effects:
Estimate Std. Error z value Pr(>|z|)
(Intercept) -2.58787 0.27034 -9.573 < 2e-16 ***
taskpriming 1.47193 0.33943 4.336 1.45e-05 ***
cent_Proficiency -0.06246 0.02659 -2.349 0.01884 *
taskpriming:cent_Proficiency 0.08935 0.03235 2.762 0.00575 **
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Correlation of Fixed Effects:
(Intr) tskprm cnt_Pr
taskpriming -0.685
cnt_Prfcncy 0.123 -0.087
tskprmng:_P -0.107 0.076 -0.730
Interpreting the coefficient for cent_Proficiency, it looks like the log
odds of a correct response decrease by .06, signalled by the - sign, when
the task is the AJT (default level), for each unit increase in proficiency.
This effect is mildly significant at the p <.05 level.
Here is the dilemma. If I graph the results I obtain the plot in attachment
where the probability in the AJT of a correct answer (coded as 1) is
actually the other way around, that is directly proportional to proficiency.
The R script for the ggplot is taken from the last page of the VCD package,
reported here for convenience in its original:
> ggplot(Donner, aes(age, survived, color = sex)) +
+ geom_point(position = position_jitter(height = 0.02, width = 0)) +
+ stat_smooth(method = "glm", family = binomial, formula = y ~ x,
+ alpha = 0.2, size=2, aes(fill = sex))
What am I to make of this?
Best,
Francesco
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