Anova II table, df, drop1 and very complex regression models!

Good morning,


I have complex data of 7 variables (6 treatment + 1 control [?age? in the
model below]) plus 18 interactions in a dataset of 2448 observations which
have some missing values (NAs).  The maximal model which I have simplified
as per y hypothesis is as follows.



modelAAW<-glmer(match~Listgp + vowel.quality + stimulus.presentation +
context +length + age + freq.+ Listgp:context+ Listgp:length+ Listgp:freq.+
Listgp:stimulus.presentation+ Listgp:age+ context:length+ context:freq.+
context:stimulus.presentation+ context:age+ length:freq.+
length:stimulus.presentation+ length:age+ freq.:stimulus.presentation+
freq.:age+ stimulus.presentation:age+  Listgp:stimulus.presentation +
Listgp:vowel.quality + stimulus.presentation:vowel.quality +
(Listgp|stimulus) + (stimulus.presentation+vowel.quality|listener) , data
=
SBAAW, family = "binomial", control=glmerControl(optCtrl=
list(maxfun=2e5)),
nAGQ =1)



I ran a binomial logistic regression analysis on the data and did the
stepwise regression manually since the drop1(modelAAW, test = "Chisq")
command yielded no results in a span of more than 16 hours. The resulting
regression models are nested in the maximal model (modelAAW).



Then, I reached the model selection step where I have to interpret the
anova table below which has degrees of freedom of zero for some models.



         Df    AIC    BIC  logLik deviance  Chisq Chi Df Pr(>Chisq)

AAWXI    49 2454.5 2738.8 -1178.2   2356.5

AAWXII   49 2456.4 2740.8 -1179.2   2358.4 0.0000      0     1.0000

AAWXIII  49 2456.4 2740.8 -1179.2   2358.4 0.0000      0     1.0000

AAWIX    51 2457.6 2753.5 -1177.8   2355.6 2.8749      2     0.2375

AAWX     51 2457.6 2753.5 -1177.8   2355.6 0.0000      0     1.0000

AAWVI    52 2458.6 2760.4 -1177.3   2354.6 0.9410      1     0.3320

AAWVII   52 2458.6 2760.4 -1177.3   2354.6 0.0075      0     <2e-16 ***

AAWVIII  52 2458.6 2760.3 -1177.3   2354.6 0.0094      0     <2e-16 ***

AAWV     54 2458.4 2771.7 -1175.2   2350.4 4.2412      2     0.1200

AAWIII   56 2461.9 2786.9 -1175.0   2349.9 0.4275      2     0.8076

AAWIV    56 2461.9 2786.9 -1175.0   2349.9 0.0000      0     1.0000

AAWII    57 2463.9 2794.7 -1175.0   2349.9 0.0215      1     0.8835

AAWI     60 2467.9 2816.1 -1174.0   2347.9 1.9763      3     0.5773

modelAAW 66 2474.4 2857.3 -1171.2   2342.4 5.5778      6     0.4721

Signif. codes:  0 ?***? 0.001 ?**? 0.01 ?*? 0.05 ?.? 0.1 ? ? 1





So many people that I have consulted tell me that I shouldn?t trust a model
of df=zero and advise that I should re-run the models using the drop1
command or simplify the maximal model but in my case I don?t know if I will
ever get results especially that it took more than 16 hours straight with
no luck and I simplified the maximal model to the best I could.



When I checked R documentation, I read that ?when given a sequence of
objects, anova tests the models against one another in the order specified?
based on the AIC value from the smallest to the largest.  However, there
is  a warning that ?the comparison between two or more models will only be
valid if they are fitted to the same dataset. This may be a problem if
there are missing values and R's default of na.action = na.omit is used?,
so I?m assuming this is the case with my models.



Now, should I select model AAWVIII since it has the least p-value (and the
least BIC value compared to AAWVII)?



The formulas of the two models in addition to AAWXI model are as follows.
The first two models are similar to each other except that in AAWVIII the
variable stimulus.presentation is deleted and in model AAWXI the variable
Listgp is deleted.


AAWVI<-glmer(match~Listgp + vowel.quality + stimulus.presentation + context
+ age + freq.+ Listgp:freq.+ Listgp:stimulus.presentation+ context:length+
context:freq.+ context:stimulus.presentation+length:stimulus.presentation+
length:age+ freq.:stimulus.presentation+ freq.:age+
stimulus.presentation:age+ + Listgp:stimulus.presentation +
Listgp:vowel.quality + stimulus.presentation:vowel.quality +
(Listgp|stimulus) + (stimulus.presentation+vowel.quality|listener) , data
=
SBAAW, family = "binomial", control=glmerControl(optCtrl=
list(maxfun=2e5)),
nAGQ =1)



AAWVIII<-glmer(match~Listgp + vowel.quality + context + age + Listgp:freq.+
Listgp:stimulus.presentation+ context:length+ context:freq.+
context:stimulus.presentation+length:stimulus.presentation+ length:age+
freq.:stimulus.presentation+ freq.:age+ stimulus.presentation:age+ +
Listgp:stimulus.presentation + Listgp:vowel.quality +
stimulus.presentation:vowel.quality + (Listgp|stimulus) +
(stimulus.presentation+vowel.quality|listener) , data = SBAAW, family =
"binomial", control=glmerControl(optCtrl=list(maxfun=2e5)), nAGQ =1)



AAWXI<-glmer(match~vowel.quality + context + age + Listgp:freq.+
Listgp:stimulus.presentation+ context:length+ context:freq.+
context:stimulus.presentation+length:stimulus.presentation+
freq.:stimulus.presentation+ freq.:age+ stimulus.presentation:age+ +
Listgp:stimulus.presentation + Listgp:vowel.quality +
stimulus.presentation:vowel.quality + (Listgp|stimulus) +
(stimulus.presentation+vowel.quality|listener) , data = SBAAW, family =
"binomial", control=glmerControl(optCtrl=list(maxfun=2e5)), nAGQ =1)



I would appreciate your help with this.



--
Shadiya

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