# CI's from full model-averaged coefficients from model.avg (MuMIn package) [closed]

I am currently trying to get model-averaged estimates (and confidence intervals) for a GLMM I am running.

After obtaining a full set of candidate models using the dredge() function from the MuMIn package in R and selecting the 95% confidence set using:

avgmod.95 <- model.avg(all.mod, subset = cumsum(weight) <= .95)


'summary(avgmod.95)' gives me both the full and conditional parameter estimates (see below output of the reproducible example). The full estimates treat every parameter equally and averages them over all models (i.e., even those not containing the parameter, for which it gives the parameter a value of 0). These are the parameter estimates I'd like to report.

So far so good, but I'd also like to report confidence intervals. Running the function confint(avgmod.95) (as suggested in several papers) gives one confidence interval for each parameter (see reproducible example output below). However, these confidence intervals match the conditional parameter estimates much more closely than they do the full parameter estimates (which I am interested in).

My questions are:

• Does the object generated with model.avg() only produce one set of confidence intervals, or does confint() give confidence intervals based on the conditional averages only?
• If the latter is the case, is there a way around this to obtain CI's for the full averages?

Here's a reproducible example using the mtcars data:

require(lme4)
require(MuMIn)

# Fit the global model
global.model <- lmer(mpg ~ hp + drat*wt + (1|gear), data=mtcars)

# Set na.action to na.fail for dredge function to run
options(na.action="na.fail")

# Generate full model set
dr <- dredge(global.model)

# Generate model average values of 95% confidence set of models
avgmod.95 <- model.avg(dr, subset = cumsum(weight) <= .95)

# Get a summary of model averaged values (both full and conditional)
summary(avgmod.95)

# Get CI's for model parameter averages
confint(avgmod.95)


Now summary(avgmod.95) gives:

Call:
model.avg.model.selection(object = dr, subset = cumsum(weight) <=
0.95)

Component model call:
lmer(formula = mpg ~ <4 unique rhs>, data = mtcars)

Component models:
df logLik   AICc delta weight
134   6 -73.31 161.97  0.00   0.76
1234  7 -73.53 165.73  3.75   0.12
13    5 -77.29 166.89  4.92   0.07
123   6 -75.89 167.14  5.16   0.06

Term codes:
drat      hp      wt drat:wt
1       2       3       4

Model-averaged coefficients:
(full average)
Estimate Std. Error Adjusted SE z value Pr(>|z|)
(Intercept) 11.208222  13.650695   14.120116   0.794   0.4273
drat         6.851292   3.665723    3.784583   1.810   0.0702 .
wt           3.244549   4.455566    4.586870   0.707   0.4793
drat:wt     -2.276614   1.341948    1.377762   1.652   0.0985 .
hp          -0.005121   0.011796    0.011856   0.432   0.6658

(conditional average)
Estimate Std. Error Adjusted SE z value Pr(>|z|)
(Intercept) 11.208222  13.650695   14.120116   0.794  0.42733
drat         6.851292   3.665723    3.784583   1.810  0.07025 .
wt           3.244549   4.455566    4.586870   0.707  0.47935
drat:wt     -2.594754   1.107692    1.156718   2.243  0.02488 *
hp          -0.029439   0.009162    0.009600   3.066  0.00217 **
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Relative variable importance:
drat wt   drat:wt hp
Importance:          1.00 1.00 0.88    0.17
N containing models:    4    4    2       2


and confint(avgmod.95) gives:

                   2.5 %      97.5 %
(Intercept) -16.46669809 38.88314109
drat         -0.56635437 14.26893779
wt           -5.74555075 12.23464840
drat:wt      -4.86187937 -0.32762871
hp           -0.04825531 -0.01062219


Notice how the CI's confirm the conditional averages and not the full averages from the summary output.

## closed as off-topic by gung♦, usεr11852, Sven Hohenstein, mpiktas, Sean EasterNov 13 '15 at 14:19

• This question does not appear to be about statistics within the scope defined in the help center.
If this question can be reworded to fit the rules in the help center, please edit the question.

• Apologies. I am new to this site and didn't think of adding an example to this question. Hope the update helps! – TBird Nov 15 '15 at 22:39
• Is the question still too off-topic, or can it be voted for reopening? – TBird Nov 16 '15 at 21:13
• It depends on the intent of "way around this": are you looking for an R programming solution or for a statistical explanation, possibly with formulas or alternative approaches? – whuber Nov 17 '15 at 14:00
• Use the argument full = TRUE i.e. confint(avgmod.95, full = T) – user2390246 Jun 17 '16 at 13:28