[R] mgcv::gam(): NA parametric coefficient in a model with two categorical variables + model interpretation

[Fotis Fotiadis]

Dear Prof. Wood

Thank you, again, for your immediate response.

Best,
Fotis

On Mon, May 23, 2016 at 4:32 PM, Simon Wood <simon.wood at bath.edu> wrote:

> Q1: It looks like the model is not fully identifiably given the data and
> as a result igcCAT.ideo has been set to zero - there is no sensible test to
> conduct with such a term, hence the NAs in the test stat an p-value fields.
>
> Q2: A separate (centred) smooth is estimated for each level of igc. If you
> want a baseline (igcCAT.pseudo) smooth, and difference smooths for the rest
> of the levels of igc then you need to set igc to be an ordered factor, and
> use something like...
> ~ igc + s(ctrial) + s(ctrial,by=igc)
> - see section on `by' variables in ?gam.models.
>
> best,
> Simon
>
>
> On 22/05/16 23:29, Fotis Fotiadis wrote:
>
>> Hallo all
>>
>> I am using a gam model for my data.
>>
>> m2.4<-bam(acc~ 1 + igc + s(ctrial, by=igc) + shape + s(ctrial, by=shape) +
>> s(ctrial, sbj, bs = "fs", m = 1) , data=data, family=binomial)
>>
>> igc codes condition and there are four levels (CAT.pseudo,
>> CAT.ideo,PA.pseudo, PA.ideo), and shape is a factor (that cannot be
>> considered random effect) with four levels too (rand21, rand22, rand23,
>> rand30).
>>
>> Here is the summary of the model
>>
>>> summary(m2.4)
>>>
>> Family: binomial
>> Link function: logit
>>
>> Formula:
>> acc ~ 1 + igc + s(ctrial, by = igc) + shape + s(ctrial, by = shape) +
>>      s(ctrial, sbj, bs = "fs", m = 1)
>>
>> Parametric coefficients:
>>               Estimate Std. Error z value Pr(>|z|)
>> (Intercept)    3.5321     0.1930  18.302  < 2e-16 ***
>> igcCAT.ideo    0.0000     0.0000      NA       NA
>> igcPA.ideo    -0.3650     0.2441  -1.495   0.1348
>> igcPA.pseudo  -0.2708     0.2574  -1.052   0.2928
>> shaperand22   -0.1390     0.1548  -0.898   0.3693
>> shaperand23    0.3046     0.1670   1.823   0.0682 .
>> shaperand30   -0.5839     0.1163  -5.020 5.16e-07 ***
>> ---
>> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
>>
>> Approximate significance of smooth terms:
>>                              edf  Ref.df   Chi.sq  p-value
>> s(ctrial):igcCAT.pseudo   3.902   4.853   74.787 1.07e-14 ***
>> s(ctrial):igcCAT.ideo     2.293   2.702   13.794 0.001750 **
>> s(ctrial):igcPA.ideo      1.000   1.000   11.391 0.000738 ***
>> s(ctrial):igcPA.pseudo    3.158   3.815   20.411 0.000413 ***
>> s(ctrial):shaperand21     2.556   3.316   31.387 1.46e-06 ***
>> s(ctrial):shaperand22     1.000   1.000    0.898 0.343381
>> s(ctrial):shaperand23     2.304   2.850    6.144 0.118531
>> s(ctrial):shaperand30     4.952   5.947   27.806 0.000144 ***
>> s(ctrial,sbj)           221.476 574.000 1502.779  < 2e-16 ***
>> ---
>> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
>>
>> Rank: 652/655
>> R-sq.(adj) =  0.405   Deviance explained = 43.9%
>> fREML =  24003  Scale est. = 1         n = 18417
>>
>>
>> I am not sure how this model works, but I guess it creates four smooths
>> for
>> each level of condition, and four smooths for each level of shape.
>>
>> There is also the intercept of the model, set at the reference level of
>> condition (CAT.pseudo) and at the reference level of shape (rand21). Each
>> parametric term represents the difference of each level of each of the two
>> factors from the intercept.
>>
>> I have two questions
>>
>> Q1:
>> Does anyone now why I get NA results in the second line of the parametric
>> terms?
>>
>> Q2:
>> The term igcCAT.ideo denotes the difference in the intercept between
>> (A): condition=igcCAT.ideo,  and
>> (B): (condition=igcCATpseudo ) &(shape=rand21).
>> But what is the value (level) of shape for (A)?
>> Is it the reference level? Or is it, perhaps, the "grand mean" of the
>> shape
>> variable?
>>
>>
>> Thank you in advance for your time,
>> Fotis
>>
>>
>>
>
> --
> Simon Wood, School of Mathematics, University of Bristol BS8 1TW UK
> +44 (0)117 33 18273     http://www.maths.bris.ac.uk/~sw15190
>
>


-- 
PhD Candidate
Department of Philosophy and History of Science
University of Athens, Greece.
http://users.uoa.gr/~aprotopapas/LLL/en/members.html#fotisfotiadis

Notice: Please do not use this account for social networks invitations, for
sending chain-mails to me, or as it were a facebook account. Thank you for
respecting my privacy.

	[[alternative HTML version deleted]]