Can AIC decrease when "significant" predictors are swapped out for "nonsignificant" ones?

[Walter Piper]

I will apologize in advance if the subject matter in my question is inappropriate. This is my first attempted post, though I have learned enormously from the posts of others and responses to them.

I am using -mixed- to model predictors of date of hatching date for an aquatic bird in a long-term study. Females who lay the eggs are sampled in the dataset across years, so I have included female identity as a random effect. My command is:

mixed hatchasdoyfixed iceout lnlksize blackfly FTERR15vsrest FTERR15vsrestSQ if Fembargo>5 || female:, nolog

Mixed-effects ML regression Number of obs = 864
Group variable: female Number of groups = 248
Obs per group:
min = 1
avg = 3.5
max = 16
Wald chi2(5) = 182.53
Log likelihood = -3226.5848 Prob > chi2 = 0.0000

---------------------------------------------------------------------------------
hatchasdoyfixed | Coefficient Std. err. z P>|z| [95% conf. interval]
----------------+----------------------------------------------------------------
iceout | .2386255 .0260036 9.18 0.000 .1876594 .2895917
lnlksize | -1.294213 .4755676 -2.72 0.007 -2.226309 -.3621178
blackfly | 13.28497 2.271379 5.85 0.000 8.833144 17.73679
FTERR15vsrest | -3.578299 .8136812 -4.40 0.000 -5.173085 -1.983513
FTERR15vsrestSQ | .504285 .1464524 3.44 0.001 .2172435 .7913265
_cons | 172.937 2.073477 83.40 0.000 168.8731 177.001
---------------------------------------------------------------------------------

------------------------------------------------------------------------------
Random-effects parameters | Estimate Std. err. [95% conf. interval]
-----------------------------+------------------------------------------------
female: Identity |
var(_cons) | 20.34735 4.554122 13.12179 31.55171
-----------------------------+------------------------------------------------
var(Residual) | 87.82712 4.882628 78.76028 97.93773
------------------------------------------------------------------------------
LR test vs. linear model: chibar2(01) = 42.05 Prob >= chibar2 = 0.0000

. estat ic

Akaike's information criterion and Bayesian information criterion

-----------------------------------------------------------------------------
Model | N ll(null) ll(model) df AIC BIC
-------------+---------------------------------------------------------------
. | 864 . -3226.585 8 6469.17 6507.262

hatchasdoyfixed is the day of year when hatching occurs; iceout, lnlksize, and blackfly are continuous covariates affecting hatching date.
FTERR15vsrest is the number of years a female has resided on the current territory, with a threshold of 5 years (i.e. 5+ years is coded as "5")
FTERR15vsrestSQ is just the square of FTERR15vsrest.

All is fine so far. Hatching date declines for the first few years on a territory but then increases after 5-10 years on a territory (probably owing to senescence). This makes sense in the system and is similar to what many other birds show.

But when I run a model that is similar, except that I have substituted the two predictors FTERR12vsrest and FTERR12vsrestSQ (threshold set at two years, not five) for FTERR15vsrest and FTERR15vsrestSQ, I get this result:

mixed hatchasdoyfixed iceout lnlksize blackfly FTERR12vsrest FTERR12vsrestSQ if Fembargo>5 || female:, nolog

Mixed-effects ML regression Number of obs = 864
Group variable: female Number of groups = 248
Obs per group:
min = 1
avg = 3.5
max = 16
Wald chi2(5) = 184.19
Log likelihood = -3225.8934 Prob > chi2 = 0.0000

---------------------------------------------------------------------------------
hatchasdoyfixed | Coefficient Std. err. z P>|z| [95% conf. interval]
----------------+----------------------------------------------------------------
iceout | .2388632 .0259866 9.19 0.000 .1879304 .2897961
lnlksize | -1.316448 .4744776 -2.77 0.006 -2.246407 -.3864886
blackfly | 13.36963 2.272566 5.88 0.000 8.915487 17.82378
FTERR12vsrest | -2.643817 2.238305 -1.18 0.238 -7.030815 1.743182
FTERR12vsrestSQ | -.0655009 1.019983 -0.06 0.949 -2.064631 1.933629
_cons | 172.9939 2.116142 81.75 0.000 168.8463 177.1415
---------------------------------------------------------------------------------

------------------------------------------------------------------------------
Random-effects parameters | Estimate Std. err. [95% conf. interval]
-----------------------------+------------------------------------------------
female: Identity |
var(_cons) | 20.36309 4.54509 13.14781 31.53798
-----------------------------+------------------------------------------------
var(Residual) | 87.66014 4.871796 78.61326 97.74814
------------------------------------------------------------------------------
LR test vs. linear model: chibar2(01) = 42.41 Prob >= chibar2 = 0.0000

. estat ic

Akaike's information criterion and Bayesian information criterion

-----------------------------------------------------------------------------
Model | N ll(null) ll(model) df AIC BIC
-------------+---------------------------------------------------------------
. | 864 . -3225.893 8 6467.787 6505.879

In short, AIC has decreased slightly when I swapped out two "good" predictors for two "poor" ones.

I am puzzled by this result -- and have stalled on my analysis -- because I am using AIC to try to find the best predictors from among a set of plausible ones. FTERR12vsrest and FTERR15vsrest are equally plausible.

Thanks for any insights you can provide me. I am sorry if this is more of a statistics question than a STATA question.

Walter Piper

[Carlo Lazzaro]

Walter:
welcome to the Statalist.
As per FAQ, please post your query on the General forum (using CODE delimiters, please, to share what you typed and what Stata gave you back). Thanks.