[R-sig-ME] Orthogonal Polynomial contrasts with ordered factors
Quentin Schorpp
quentin.schorpp at ti.bund.de
Thu Dec 17 09:08:37 CET 2015
Hello,
Thank you for your answer. If I understood you right, you mean
significant effects of higher order polynomials could point to
non-linear relationships between response and explanatory variable (also
if the explanator is a categorial factor), under the condition, that
lower order polynomials in between are "skipped" in the sense that
theses are not significant? The significant effect of ("non successive")
higher order polynomials could be either in interaction terms and
without? However when thinking about fitting a non-linear model, i'm
wondering if it would be justified in the case that significant ("non
successive") higher order polynomials only occur in one interaction case
(the discussed pattern is only observed in the interaction with one
level of the second interaction factor).
p.S. Sorry for the worse formatting of the initial question, while
writing the e-mail everything looked good, especially the factor by
factor table to reveal the partly nested structure.
kind regards,
Quentin
Am 16.12.2015 um 12:38 schrieb Steve Denham:
> I'll take a crack at the B questions. Keep in mind that this is an
> opinion only. A significant fourth order by other factor interaction,
> especially when the lower order polynomial by factor interactions are
> not significant means that you have probably fit a polynomial to a
> non-polynomial effect. Your mention of a plateau tends to support
> this, at least to me. Some sort of non-linear effect (sigmoidal, four
> or five factor logistic) may make more sense from a biological
> perspective.
> Steve Denham Director, Biostatistics MPI Research, Inc.
>
> ------------------------------------------------------------------------
> *From:* Quentin Schorpp <quentin.schorpp at ti.bund.de>
> *To:* "r-sig-mixed-models at r-project.org"
> <r-sig-mixed-models at r-project.org>
> *Sent:* Tuesday, December 15, 2015 8:14 AM
> *Subject:* [R-sig-ME] Orthogonal Polynomial contrasts with ordered
> factors
>
> Hello,
>
> I would appreciate to get to know more about the use of polynomial
> contrasts in lme4::glmer.
> Does anybody could give me an advice for literature about that
> subject.
>
> In particular
> A: I read, that if a second order polynomial is significant in the
> summary output, then it is supposed to be significant AFTER the first
> order polynomial was taken into account. Is that right?
>
> B1 : What happens if i use an ordered factor with another factor
> (ordered or not) in an itneraction term? What does a signficant
> interaction of the second factor (any level) with the
> fourth power polynomial of the first ordered factor tell me?
> B2: And waht does it tell me when the lower order polynomials are not
> significant in the interaction?
>
>
> For more interested readers:
>
> _The data_
> My data is abundances of earthworms. I sampled 15 fields, three times
> (samcam) during two years, with 4 pseudoreplicates per field (N=180).
> The factor age_class describes the stage of development of the
> field, it
> has 5 levels ((n = 3 replicates).
> However, one of these levels A_Cm has n=6 since i had to switch the
> fields in the second year.
> Field.ID is my random factor, to control for the pseudoreplication
> per
> field and the longitudinal character of the data. For the sake of
> less
> complexity samcam stayed non-ordered.
>
> Here is the design
>
> field.ID\samcam1 2 3 1 4 4 4 2 4 4 4 3 4 4 4 4 4 4 4 5 4 4 4 6 4
> 4 4 7 4
> 4 4 8 4 4 4 9 4 4 4 10 4 4 4 11 4 4 4 _12 4 4 4_ 13 4 0 0 Fields
> had to
> be switched in the second year 14 4 0 0 15 4 0 0 16 0 4 4 17 0 4 4
> 18 0 4 4
>
>
>
> Other continuous predictor variables were scaled before analysis.
>
> data structure:
> $ abundance : num 0 0 3 3 2 1 2 5 12 5 ...
>
> $ ID : Factor w/ 180 levels "1","2","3","4",..: 1 2 3
> 4 5
> 6 7 8 9 10 ...
> $ field.ID : Factor w/ 18 levels "1","2","3","4",..: 1 1 1
> 1 2 2
> 2 2 3 3 ...
> $ age_class : Ord.factor w/ 5 levels
> "A_Cm"<"B_Sp_young"<..: 5 5
> 5 5 5 5 5 5 5 5 ...
> $ samcam : Factor w/ 3 levels "1","2","3": 1 1 1 1 1 1 1
> 1 1 1 ...
> $ hole : Factor w/ 4 levels "1","2","3","4": 1 2 3 4 1
> 2 3 4
> 1 2 ...
>
> $ scl.pH : num -1.553 -1.553 -1.553 -1.553 0.715 ...
> $ scl.mc : num -1.072 -1.072 -1.072 -1.072 -0.429 ...
> $ scl.cn : num -0.703 -0.703 -0.703 -0.703 -0.474 ...
> $ scl.sand : num -0.245 -0.245 -0.245 -0.245 -0.0127 ...
> $ scl.silt : num -0.897 -0.897 -0.897 -0.897 -1.529 ...
> $ scl.clay : num 1.19 1.19 1.19 1.19 1.66 ...
> $ scl.ata1 : num 1.6471 1.6471 1.6471 1.6471 0.0894 ...
> $ scl.atb1 : num 1.6658 1.6658 1.6658 1.6658 0.0659 ...
> $ scl.hum1 : num -1.378 -1.378 -1.378 -1.378 0.429 ...
>
> _my hyptheses are_
> 1. abundance increases with increasing age_class
> 2. If abundance increases over the age classes it will be observed by
> increasing abundance during the period of sampling
> (3. Abundance increases during the period of sampling)
>
> _The Model was :_
> best.mod <- glmer(abundance~ age_class*samcam + scl.prec1 +
> scl.mc*scl.pH + (1|field.ID) ,data=data,family=poisson,
> control=glmerControl(optimizer="bobyqa"))
>
> here is The Model output of one of the best models revealed by
> MuMIn::dredge:
>
> Generalized linear mixed model fit by maximum likelihood (Laplace
> Approximation) ['glmerMod']
> Family: poisson ( log )
> Formula: anc ~ age_class * samcam + I(scl.ats1^2) + scl.prec1 + (1
> | field.ID)
> Data: data
> Control: glmerControl(optimizer = "bobyqa")
>
> AIC BIC logLik deviance df.resid
> 731 789 -348 695 162
>
> Scaled residuals:
> Min 1Q Median 3Q Max
> -2.181 -0.696 -0.171 0.644 4.178
>
> Random effects:
> Groups Name Variance Std.Dev.
> field.ID (Intercept) 0.263 0.513
> Number of obs: 180, groups: field.ID, 18
>
> Fixed effects:
> Estimate Std. Error z value Pr(>|z|)
> (Intercept) 0.6457 0.2079 3.11 0.0019 **
> age_class.L 1.9924 0.4416 4.51 6.4e-06 ***
> age_class.Q -0.8644 0.4204 -2.06 0.0398 *
> age_class.C -0.2373 0.4007 -0.59 0.5537
> age_class^4 0.7026 0.3591 1.96 0.0504 .
> samcam2 0.8549 0.2074 4.12 3.7e-05 ***
> samcam3 0.3074 0.1852 1.66 0.0969 .
> I(scl.ats1^2) -0.3328 0.1038 -3.21 0.0013 **
> scl.prec1 0.2241 0.0851 2.63 0.0085 **
> age_class.L:samcam2 -0.3474 0.5463 -0.64 0.5248
> age_class.Q:samcam2 0.1074 0.4766 0.23 0.8216
> age_class.C:samcam2 0.8910 0.3644 2.44 0.0145 *
> _age_class^4:samcam2 -1.0352 0.2601 -3.98 6.9e-05 *** _ # HERE is
> the significant interaction of interest!
> age_class.L:samcam3 0.1274 0.5125 0.25 0.8038
> age_class.Q:samcam3 -0.1801 0.4429 -0.41 0.6842
> age_class.C:samcam3 0.5659 0.3615 1.57 0.1174
> _age_class^4:samcam3 -0.6489 0.2617 -2.48 0.0131 * ___# HERE is
> the significant interaction of interest!
>
>
> _Interpretation:_
> I understood, that the relationship was linear in general, as
> indicated
> by the second line of the output, and this did not change between the
> sampling campaigns. However, during the second and third sampling
> campaign the relationship of abundances in the age_classes was
> characterised by a stronger slope in younger classes and reached a
> plateau afterwards, as indicated by the fourth power.
> The missing of the interaction between age_class and samcam1 is very
> hard for me to understand
>
> I'm thankful for any advices!
>
> Quentin
>
>
> --
> Quentin Schorpp, M.Sc.
> Thünen-Institut für Biodiversität
> Bundesallee 50
> 38116 Braunschweig (Germany)
>
> Tel: +49 531 596-2524
> Fax: +49 531 596-2599
> Mail: quentin.schorpp at ti.bund.de <mailto:quentin.schorpp at ti.bund.de>
> Web: http://www.ti.bund.de <http://www.ti.bund.de/>
>
> Das Johann Heinrich von Thünen-Institut, Bundesforschungsinstitut
> für Ländliche Räume, Wald und Fischerei – kurz: Thünen-Institut –
> besteht aus 15 Fachinstituten, die in den Bereichen Ökonomie,
> Ökologie und Technologie forschen und die Politik beraten.
>
> Quentin Schorpp, M.Sc.
> Thünen Institute of Biodiversity
> Bundesallee 50
> 38116 Braunschweig (Germany)
>
> Tel: +49 531 596-2524
> Fax: +49 531 596-2599
> Mail: quentin.schorpp at ti.bund.de <mailto:quentin.schorpp at ti.bund.de>
> Web: http://www.ti.bund.de <http://www.ti.bund.de/>
>
> The Johann Heinrich von Thünen Institute, Federal Research
> Institute for Rural Areas, Forestry and Fisheries – Thünen
> Institute in brief –
> consists of 15 specialized institutes that carry out research and
> provide policy advice in the fields of economy, ecology and
> technology.
>
>
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>
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--
Quentin Schorpp, M.Sc.
Thünen-Institut für Biodiversität
Bundesallee 50
38116 Braunschweig (Germany)
Tel: +49 531 596-2524
Fax: +49 531 596-2599
Mail: quentin.schorpp at ti.bund.de
Web: http://www.ti.bund.de
Das Johann Heinrich von Thünen-Institut, Bundesforschungsinstitut für Ländliche Räume, Wald und Fischerei – kurz: Thünen-Institut –
besteht aus 15 Fachinstituten, die in den Bereichen Ökonomie, Ökologie und Technologie forschen und die Politik beraten.
Quentin Schorpp, M.Sc.
Thünen Institute of Biodiversity
Bundesallee 50
38116 Braunschweig (Germany)
Tel: +49 531 596-2524
Fax: +49 531 596-2599
Mail: quentin.schorpp at ti.bund.de
Web: http://www.ti.bund.de
The Johann Heinrich von Thünen Institute, Federal Research Institute for Rural Areas, Forestry and Fisheries – Thünen Institute in brief –
consists of 15 specialized institutes that carry out research and provide policy advice in the fields of economy, ecology and technology.
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