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

[Francesco Sigona]

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) 
<http://www.cril.unisalento.it> &
Cognitive Neuroscience of Language and Speech Sciences Lab (CNLSS) * 	
*Dipartimento di Studi umanistici
Università del Salento * 	

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*Laboratorio Diffuso di Ricerca Interdisciplinare Applicata alla Medicina
(DReAM) *