[R-sig-ME] main effect significance disappears when interaction is modeled

[Thierry Onkelinx]

Dear Francesco,

It's not possible to get a significance of a main effect when it is part
from an interaction. See e.f. fortunes::fortune(55)

Your comparison in a) is the same model but with a different
parametrisation.

I'd report an estimate of the effect for each combination of height and
place, given that both are categorical. Use multcomp to get those or fit a
model like X~0 + HEIGHT:PLACE +  LOWNESS + (1|Soggetto) Yet another
parametrisation of the same model. These will directly estimate the effect
of each height/place interaction.

Best regards,

ir. Thierry Onkelinx
Instituut voor natuur- en bosonderzoek / Research Institute for Nature and
Forest
team Biometrie & Kwaliteitszorg / team Biometrics & Quality Assurance
Kliniekstraat 25
1070 Anderlecht
Belgium

To call in the statistician after the experiment is done may be no more
than asking him to perform a post-mortem examination: he may be able to say
what the experiment died of. ~ Sir Ronald Aylmer Fisher
The plural of anecdote is not data. ~ Roger Brinner
The combination of some data and an aching desire for an answer does not
ensure that a reasonable answer can be extracted from a given body of data.
~ John Tukey

2015-10-30 13:48 GMT+01:00 Francesco Sigona <francesco.sigona op unisalento.it>
:

> Hi all,
>
> I've searching the list but I could't find an answer.
>
> In my design, where all my 3 fixed effects are categorical (binary), I
> found that HEIGHT is significant (also anova tell me the same), when I
> model main effects only.
>
> STUDYING MODEL: X ~ HEIGHT + LOWNESS + PLACE + (1|Soggetto)
>               Estimate Std. Error    t value
> (Intercept) -52.204545   1.277885 -40.852292
> HEIGHThigh    3.681818   1.475575   2.495175
> LOWNESSlow   -7.386364   1.952002  -3.783994
> PLACEback    -0.500000   1.475575  -0.338851
>
> also, I get that  :
> LOWNESS affected X (Chi2(1)=13.61, p=0.00023) adding about -7.39 ± 2
> (standard error) to it
> HEIGHT affected X (Chi2(1)=6.335, p=0.012) adding about 3.68 ± 1.5
> (standard error) to it
>
> (despite the names, LOWNESS is not the opposite of HEIGHT)
>
> Then, if try to model the interaction between PLACE and HEIGHT this comes
> out:
> STUDYING MODEL WITH INTERACTIONS:  X~LOWNESS + HEIGHT*PLACE + (1|Soggetto)
>                        Estimate Std. Error    t value
> (Intercept)          -48.909091   1.162784 -42.062068
> LOWNESSlow            -4.090909   1.520004  -2.691380
> HEIGHThigh            -2.909091   1.520004  -1.913870
> PLACEback             -7.090909   1.520004  -4.665058
> HEIGHThigh:PLACEback  13.181818   2.149611   6.132188
> ************HEIGHT*PLACE affected X (Chi2(1)=29.17, p=6.6e-08)
>
> (then I am supposed to report the post-hoc that I would get by means of
> multcomp package.)
>
> This posits the following questions to me:
>
> a) Does HEIGHT is still significant? If I make an anova() comparison
> between X~LOWNESS + HEIGHT + PLACE + HEIGHT:PLACE +  (1|Soggetto) and
> X~LOWNESS + PLACE + HEIGHT:PLACE +  (1|Soggetto),    anova() thinks that
> the two models are the same.
>
> b) Should I report that I found a main effect for HEIGHT (with 3.681818
> estimates) and an interaction with PLACE, or should I report that I found
> just the interaction?
>
> c) Since I find the interaction, in this model the main effect of LOW is
> still significant but Chi2square related stuff changes to Chisq=7.3232,
> p=0.0068), as well the slope (now is -4.09). So , what I am supposed to
> report? WHat exactly you would report in my case?
>
> I really need some direction about this, thank you in advance.
>
> Francesco
>
>
> --
> *Francesco SIGONA*
> Electronics engineer
> Piazza Filippo Muratore
> 73100 - Lecce - Italy   <
> https://maps.google.com/maps?q=40.331002,18.156462>
> tel.: +39 0832 335006
> fax.: +39 0832 335007
>
> ============================================================
> *Center for Interdisciplinary Research on Language (CRIL) <
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> *Dipartimento di Studi umanistici
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>
> ============================================================
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> (DReAM) *
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