Dear R users and experts,

I have a set of binomial data collected from a group of native speakers of
English and a group of second language learners of English (sample dataset
shown on the bottom of this email). These data concern native speakers' and
second language learners' verbal productions of three types (lists) of
two-word compound words (such as "blackboard"). Both groups of participants
had to produce the same three lists of words. If a participant placed stress
on the 1st word of a compound word, s/he would get a 1; otherwise, s/he
would get a 0.  I want to know how second language learners' performances
compare to native speakers as a function of factors such as (a) initial age
of exposure to English (AoE) (b) length of exposure to English (le), (c) age
of arriving in the United States,  (d) length of residence in the United
States (lr).

The difficulty I have with such an analysis is the data sheet. An obvious
problem is that the four factors listed above are not available for native
speakers, so if I am to include both native and nonnative speakers' data
into one dataframe, there will be missing cells for the AoE, AoA, le, and lr
columns (example on the bottom of this email). I wonder if there is any way
to deal with this problem. I thought about putting 0 for age of exposure and
age of arrival for native speakers, and their ages at the time of the
experiment as length of residence and length of exposure, but I am not sure
how these would affect the analysis because after all, I am not interested
in native speakers' age, etc, and I don't really want these kinds of
information concerning native speakers to enter the analysis.

A second issue is that, say even if this problem can be dealt with, I wonder
if lmer() is suitable for this type of analysis. I know that if I am only
interested in the interaction between compound type and native language, a
lmer model can be fitted in a relatively straightforward way :

>lmer(word1~compoundType*nativelanguage + (1|subject) + (1|word), data =
data, family = "binomial")

But I am totally at a loss about how to include the aforementioned
additional factors into the analysis. It would be great if someone could
provide some insights and help me with my problem. Thank you very much in
advance!

Best,
Xiao He

********************************************************************************
Sample dataset

nativelanguage subject     word  word1  type   AoE   AoA   le   lr
other                 S1          w1      1         T1     4       8      20
24
other                 S1          w2      1         T1     4       8      20
24
other                 S1          w3      1         T1     4       8      20
24
other                 S1          w4      0         T1     4       8      20
24
other                 S1          w5      1         T1     4       8      20
24
other                 S1          w6      1         T2     4       8      20
24
other                 S1          w7      1         T2     4       8      20
24
other                 S1          w8      0         T2     4       8      20
24
other                 S1          w9      1         T2     4       8      20
24
other                 S1          w10    1         T2     4       8      20
24
other                 S1          w11    1         T3     4       8      20
24
other                 S1          w12    0         T3     4       8      20
24
other                 S1          w13    1         T3     4       8      20
24
other                 S1          w14    1         T3     4       8      20
24
other                 S1          w15    1         T3     4       8      20
24
.
.
english              S9          w1      1         T1
english              S9          w2      0         T1
english              S9          w3      0         T1
english              S9          w4      0         T1
english              S9          w5      1         T1
english              S9          w6      1         T2
english              S9          w7      0         T2
english              S9          w8      0         T2
english              S9          w9      0         T2
english              S9          w10    0         T2
english              S9          w11    1         T3
english              S9          w12    0         T3
english              S9          w13    1         T3
english              S9          w14    0         T3
english              S9          w15    1         T3





To compare native and nonnative speakers' performances on the three types of
compounds is relatively straightforward. I can fit the following model:

cp.lmer1<-lmer(word1~compoundType*nativeLanguage + (1|subject) + (1|word),
family = "binomial", data = data).

However, I am not sure how to bring in the four factors listed above (I know
that I need to examine collinearity first, but assume the four factors are
not collinear with each other). Part of the reason is that the four factors
are not





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