[R] Highly significant intercept and large standard error
Greg Snow
Greg.Snow at imail.org
Wed Oct 6 19:40:59 CEST 2010
Large coefficients and large standard errors in logistic regression models can be indicative of the Hauk-Donner phenomenon. This is where the coefficient is highly significant, but the Wald Statistic is misleading because the likelihood curve is relatively flat in the area of the estimate giving an inflated estimate of the standard error (this is documented in MASS the book (page 255 in the 3rd edition, don't know for the 4th) and the paper from 1977).
It is best to use likelihood ratio statistics instead of Wald statistics in these cases.
--
Gregory (Greg) L. Snow Ph.D.
Statistical Data Center
Intermountain Healthcare
greg.snow at imail.org
801.408.8111
> -----Original Message-----
> From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-
> project.org] On Behalf Of Sam
> Sent: Wednesday, October 06, 2010 6:03 AM
> To: r-help at r-project.org
> Subject: [R] Highly significant intercept and large standard error
>
> Dear list,
>
> I am running a lmer model and have a question.
>
> When ever i put a factor (Mag) in my model it lowers the AIC of the
> model, however the intercept is the only value with significant p-
> value. I have looked at the coefficients and the standard error and
> something jumps out at me.
>
>
> Estimate Std. Error z value Pr(>|z|)
> (Intercept) -1.35778 0.30917 -4.392 1.12e-05 ***
> MagNew -15.76939 1255.06372 -0.013 0.990
> MagOld 0.14250 0.25246 0.564 0.572
>
> MagNew relates to a categorical factor (Mag) that has 3 levels of which
> New is one and Old is another ( The third is not displayed).
>
> It appears MagNew has a huge Std.Error, what could cause this?
>
> When i do str(Mag) you will see that New is relatively rare (29 out of
> 871) i presume it is this that is raising the Std.Error value. however
> i am not sure why this is causing the intercept to have a highly
> significant p value . Furthermore how do i interpret it, I am using AIC
> values as my basis of model selection and i am unsure if this really is
> the most likely model or not?
>
> Thanks
>
> Sam
>
> [1] Old Old Old Old Old Old Old Old Old Old Old
> [12] Old Old Old Old Old Old Old Old Old Old Old
> [23] Old Old Old Mid Old Old Old Mid Old Old Old
> [34] Old Old Old Old Mid Old Old Old Old Old Old
> [45] Mid Mid Mid Old Old Old Mid Mid Mid Mid
> Old
> [56] Old Old Old Old Old Old Old Old Old Old Old
> [67] Old Old Old Old Old Old Old Old Old Old Old
> [78] Old Old Old Old Old Old Old Old Old Old Old
> [89] Old Old Old Old Old Old Old Old Old Old Old
> [100] Old Old Old Old Old Old Old Old Old New New
> [111] Old Old Old Old Old Old Old Old Old Old Mid
> [122] Mid Mid Mid Mid Old Old Old Old Mid Mid
> Mid
> [133] Mid Mid Mid Mid Mid Mid Mid Mid
> Mid Mid Mid
> [144] Mid Mid Mid Mid Old Old Old Mid Mid
> Mid Mid
> [155] Mid Mid Mid Mid Mid Mid Mid Old Old
> Old Old
> [166] Old Old Old Mid Mid Mid Mid Mid Mid
> Mid Mid
> [177] Mid Mid Mid Mid Mid Mid Mid Mid
> Mid Old Mid
> [188] Mid Mid Mid Mid Old Mid Mid Mid Mid
> Mid Mid
> [199] Mid Mid Old Old Old Old Old Old Old Old Old
> [210] Old Old Old Old Old Old Old Old Old Old Old
> [221] Old Old Old Old Old Old Old Old Old Old Old
> [232] Old Old Old Old Old Old Old Old Old Old Old
> [243] Old Old Old Old Old Old Old Old Old Old Old
> [254] Old Old Old Old Old Old Old Old Old Old Old
> [265] Old Old Old Old Old Old Old Old Old Old Old
> [276] Old Old Old Old Old Old Old Old Old Old Old
> [287] Old Old Old Old Old Old Old Old Old Old Old
> [298] Old Old Old Old Old Old Old Old Old Old Old
> [309] Old Old Old Old Old Old Old Old Old Old Old
> [320] Old Old Old Old Old Old Old Old Old Old Old
> [331] Old Old Old Old Old Old Old Old Old Old Mid
> [342] Old Old Old Old Old Old Old New New New New
> [353] New New New New New Old Old Old Old Old Old
> [364] Old New Old Old Old Old Old Old Old Old Old
> [375] Old Old Old Old Old Old Old Old Old Old Old
> [386] Old Old Old Old Old Old Old Old Mid Mid Mid
> [397] Mid Mid Mid Old Old Mid Old Old Mid Mid
> Mid
> [408] Mid Mid Mid Mid Mid Mid Mid Mid
> Mid Mid Mid
> [419] Old Old Old Old Mid Mid Mid Mid Mid Old
> Mid
> [430] Mid Mid Mid Mid Mid Mid Mid Mid
> Mid Mid Mid
> [441] Mid Mid Mid Mid Mid Mid Old Old Old
> Old Old
> [452] Old Old Old Old Old Old Old Mid Mid Old Old
> [463] Mid Mid Old Old Mid Mid Mid Mid Mid
> Old Mid
> [474] Mid Mid Old Mid Old Old Old Old Old Old Old
> [485] Mid Mid Mid Mid Mid Mid Mid Mid
> Mid Mid Old
> [496] Old Old Old Old Old Old Mid Old Mid Old Old
> [507] Old Old Old Old Old Old Old Old Old Old Old
> [518] Mid Mid Mid Mid Old Mid Old Mid Old
> Mid Mid
> [529] Old Old Mid Mid Mid Mid Mid Mid Old
> Mid Mid
> [540] Mid Mid Mid Mid Mid Mid Old Old Old
> Old Mid
> [551] Mid Mid Old Old Mid Mid Old Mid Old Old
> Old
> [562] Old Mid Old Old Old Mid Old Old Old Old Mid
> [573] Mid Mid Old Old Mid Mid Mid Mid Old
> Old Old
> [584] Mid Old Old Old Old Old Old Mid Mid Mid Old
> [595] Mid Mid Mid Old Old New Mid Mid Old Mid
> Mid
> [606] Mid Old Mid Old Old Mid Mid Mid Mid
> Mid Old
> [617] Mid Old Old Old Old Old Old Old Old Old Old
> [628] Old Old Mid Old Old Old Old Old Old Old Old
> [639] Old Old Old Old Old Old Old Old Old Old New
> [650] Old Mid Old Old Old Old Old Old Old Old Old
> [661] Old Old Old Old Old Old Old Old Old Old Old
> [672] Old Old New Old Old Old Old Old Old Old Old
> [683] New Old Old Old Old Old Old Old Old Old Old
> [694] Old Old Old Old Old Old Old Old Old Old Old
> [705] Old Old Old New Old Old New Old Old Old Old
> [716] New New New New New Old Old Old New Old Old
> [727] Old Old Old Old Old Old Mid Old Old Old New
> [738] Old Old Old Old Old Old Old Old Old Old Old
> [749] Old Old Old Old Old Old Old Old Old Old Old
> [760] New Old Old Old Old Old Old Old Old Old New
> [771] Old Old Old Old Old Old Mid Old Old New Old
> [782] Old Old Old Old Old Old Old Old Old Old Old
> [793] Old Old Old Old Old Old Old Old Old Old Old
> [804] Old Old Old Old Old Old Old Old Old Old Old
> [815] Old Old Old Old Old Old Old Old Old Old Old
> [826] Old Old Old Old Old Old Old Old Old Old Old
> [837] Old Old Old Old Old Old Old Old Old Old Old
> [848] Old Old Old Old Old Old Old Old Old Old Old
> [859] Old Old Old Old Old Old Mid Mid Old Old Old
> [870] Old Old
> Levels: Mid New Old
>
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