[R-sig-ME] Can interaction term cause Estimates and Std. Errors to be too large?
Luciano La Sala
lucianolasala at yahoo.com.ar
Sun Mar 29 20:47:04 CEST 2009
Dear R-experts,
I am running version 2.7.1 on Windows Vista. I have small dataset which consists of:
# NestID: nest indicator for each chicken. Siblings sharing the same nest have the same nest indicator.
# Chick: chick indicator consisting of a unique ID for each single chick.
# Year: 2006, 2007.
# ClutchSize: 1-, 2- , 3-eggs.
# HO: hatching order within each clutch (1, 2, 3 [first, second and third-hatched chick]).
In order to account for lack of independence at the nest level (many
chicks are nested in nest...), I'd like to run a GLMM with random slopes and intercepts for nests.
My approach to model building was as follows: Variables that had P ≤ 0.20 on their own in an initial bivariate analysis were forced into the multivariable analysis. The general procedure for model selection involved starting from a maximum model based on the bivariate analyses and eliminating terms to achieve a simpler model that only retained the significant main effects and two-way interactions. The model was restricted by stepwise manual elimination of variables using the Akaike Information Criterion (AIC) as a measure of goodness-of-fit.
Interactions were tested only between main effects which remained in the final model.
My final model for hatching failure (without testing of interaction between main effects) is:
model <- lmer(Hatching ~ HatchOrder + Year + (1|NestID), family=binomial, 1)
I get the following output:
best.model <- lmer(Hatching~HatchOrder+Year+(1|NestID), family=binomial, 1)
Generalized linear mixed model fit by the Laplace approximation
Formula: Hatching2 ~ HatchingOrder + Year1 + (1 | NestID)
Data: 1
AIC BIC logLik deviance
167.8 185.3 -78.9 157.8
Random effects:
Groups Name Variance Std. Dev.
NestID (Intercept) 1.9682 1.4029
Number of obs: 247, groups: NestID, 120
Fixed effects:
Estimate Std. Error z value Pr(>|z|)
(Intercept) -5.4800 0.8329 -6.579 4.73e-11 ***
HO_Second 1.6344 0.6841 2.389 0.01689 *
HO_Third 3.3007 0.7162 4.609 4.05e-06 ***
Year2006 2.1169 0.6741 3.140 0.00169 **
So far, so good… but then I fit the same model incorporating interaction between the main effects as follows:
interaction <-lmer(Hatching~HatchOrder+Year+HatchingOrder*Year+(1|NestID), family=binomial,1)
And I get the following output:
Data: 1
AIC BIC logLik deviance
157.8 182.3 -71.89 143.8
Random effects:
Groups Name Variance Std. Dev.
NestID (Intercept) 155.22 12.459
Number of obs: 247, groups: NestID, 120
Fixed effects:
Estimate Std. Error z value Pr(>|z|)
(Intercept) -13.6158 4.8287 -2.8198 0.00481 **
HO_Second -23.1961 36249.1930 -0.0006 0.99949
HO_Third 5.6624 2.6823 2.1110 0.03477 *
Year2006 -0.9602 6.1245 -0.1568 0.87541
HO_Second:Year2006 30.2249 36249.1931 0.0008 0.99933
HO_Third:Year2006 10.5549 5.2232 2.0208 0.04331 *
Correlation of Fixed Effects:
(Intr) HtchOS HtchOT Y12006 HOS:Y1
HtchngOrdrS 0.000
HtchngOrdrT -0.384 0.000
Year12006 -0.788 0.000 0.303
HtOS:Y12006 0.000 -1.000 0.000 0.000
HtOT:Y12006 0.197 0.000 -0.514 -0.556 0.000
Question 1: I am worried about the overly large values of the Estimate and Std. Error for "HO_Second" and "HO_Second*Year2006" from the second model (with interaction term included).
So what may me causing such large values? Should I be concerned? If so, how can I solve the problem? Is this an over-fitting problem?
Question 2: The Estimate for "Year2006" becomes negative in the second model. Any clue as to why this happens?
Question 3: Should I stick with the simpler model 1 which does not asses interaction?
Thank you in advance for the help!
Lucho
Yahoo! Cocina
Recetas prácticas y comida saludable
http://ar.mujer.yahoo.com/cocina/
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