Averaging regression output I have multiple logistic model outputs with the same predictors. The dependent response is very similar changing slightly randomly. 
I would like to take an average of the coefficients of all models. But I'm concerned that some coefficients may be large with non-significant p values and other differences. How can I get an overall average measure of effect for each predictor while considering the standard error/statistic/p-value aspects?
I thought of penalizing the coefficient each time it is not significant at a predetermined threshold. Something like:
#Edit:: This has been concluded to be the wrong way
mdl_list <- lapply(predictors, function(y) {
              tbl <- broom::tidy(glm(y, x))
              tbl$estimate <- ifelse(tbl$p.value > .05, 0, tbl$estimate)
              tbl
              }
            )

If an alternative approach to average effect exists, please point me in the right direction.
Edit
I have tried the meta-analysis in the metafor package. I even emailed the authors, they said that if this is not for summarizing multiple studies, metafor will not work.
Example: The b variables are response, the q variables are predictors.
#Data
set.seed(143)
b <- replicate(3, rbinom(8, 1, .8))
q <- replicate(4, sample(1:5, 8, TRUE))
df <- data.frame(b,q)
names(df) <- c(paste0("b",1:3), paste0("q",1:4))
#   b1 b2 b3 q1 q2 q3 q4
# 1  0  1  1  2  1  2  1
# 2  1  1  1  5  1  1  4
# 3  1  1  1  5  5  1  5
# 4  1  1  1  4  5  3  1
# 5  1  0  0  2  5  4  1
# 6  0  1  1  4  5  2  4
# 7  1  0  0  1  2  3  5
# 8  1  0  0  1  1  5  4

mdl1 <- glm(b1 ~ q1 + q2 + q3 + q4, data=df, family=binomial())
mdl2 <- glm(b2 ~ q1 + q2 + q3 + q4, data=df, family=binomial())
mdl3 <- glm(b3 ~ q1 + q2 + q3 + q4, data=df, family=binomial())

Edit 2
I may have to combine the different brands into one y variable and repeat the question responses:
y <- with(df, c(b1, b2, b3))
newdf <- df[rep(1:8,3),-(1:3)]
newdf$y <- y
head(newdf, 10)
#     q1 q2 q3 q4 y
# 1    2  1  2  1 0
# 2    5  1  1  4 1
# 3    5  5  1  5 1
# 4    4  5  3  1 1
# 5    2  5  4  1 1
# 6    4  5  2  4 0
# 7    1  2  3  5 1
# 8    1  1  5  4 1
# 1.1  2  1  2  1 1
# 2.1  5  1  1  4 1

mdl4 <- glm(y ~ q1 + q2 + q3 + q4, data=newdf, family=binomial())

The predictors q are questions like on a scale of 1-5 how much do you agree with this statement, "Store brands are just as good as name brands", "Organic foods are worth their price", "I look for discounts when I go to the supermarket".
The response variables b are questions like "Do you eat Dannon yogurt?", "Do you eat Campbell's soup?", "Do you eat at McDonald's?". 
The hypothesis is that there are some attitudes questions that are better than others at predicting brand usage. If I run a logistic regression:
$ShopMcD's = \beta_0 + \beta_1 Attitude_1 + ... + \beta_n Attitude_n$
I can see how much each question affects the log odds ratio of shopping at McDonald's. The higher ups want to see this continued for all of the food brands to see the effect each question has on brand usage overall. 
An example project delivery statement would be:
"We find that attitudes questions 2, 4, and 6 have the least effect on average over all other questions. These questions are the least predictive of food brand usage compared to others and are candidates for removal from the survey."
 A: Since you use R you might like to look at some of the packages listed in the CRAN TaskView (disclaimer, I maintain it). My personal preference is the metafor package and its author has a wealth of explanatory material on the package website. In the unlikely event that you cannot find the answer to your problems there ask again.
A: Your idea of averaging regression coefficients is ill-defined, and your new idea in the second edit is not good because it repeats datapoints in the dataset and will have underestimated uncertainties (edit: unless b1, b2, and b3 are supposed to be independent observations at the same q values, as @whuber ponders, though I get the impression otherwise). Your problem is that you don't know what effect you are trying to measure. Your question contains four explanatory variables q1, q2, q3, and q4, with three simultaneous boolean outcomes b1, b2, and b3. The only valid statistical questions you can answer with binomial regression are of the form "what is the probability of y as a function of q1 through q4, where y is a well-defined event or outcome that is related to b1, b2, and b3?" For example, y could be b1 || b2 || b3, b1 && b2 && b3, b1 && (b2 || !b3), etc. Performing different regressions for the outcomes b1, b2, and b3 using the same input data is fine, but there is no meaningful way to combine them. If you're not trying to the predict the probability of some y that can be written with b1, b2, and b3 using boolean algebra, then what are you trying to predict? Until you can answer this you have a answer in search of a question. 
