[R-sig-ME] question regarding summary output with three-way interactions
Szymek Drobniak
geralttee at gmail.com
Fri Jan 6 21:05:38 CET 2012
Hi again,
you're right. usually when terms are missing in our output - it means
the're not identifiable from our data (e.g. there's not enough
replication or specific combinations of factors are missing) - that's
why your'e getting some interactions tested after removing some other
terms. As for which terms to include - my conservative way of doing
things is to include lower terms always when I want to have higher
terms. What happens when you remove the triple interactions? Also I
wouldn;t say that interpretation of continous:categorical interactions
should be avoided in cases similar to yours: such interactions
quantify differences in betas at respective levels of the categorical
variable and provide useful valuable insight to how your response
changes with the covariate. What however should be avoided (or better
said - applied with caution) is drawing conclusions about categorical
variables (i.e. A or B in your model) if the're involved in
significant interactions with continous variables (problem similar to
heterogenous slopes in classical ANCOVA).
Cheers,
sz.
On 6 January 2012 20:40, Stefanie Kuchinsky
<stefanie.kuchinsky at gmail.com> wrote:
>
> I just realized a probable explanation.
>
> For the time3 term for which it only displayed half of the interaction term, the lower order time3:A and time3:B had been included in the model.
>
> However, there was no time4:A in the model (though there was time4:B). When I removed this effect, I now get both parts of the interaction term output [and the F test df are now correct (2, 9294) instead of (1, 9294)]. I assume that this means the higher order terms are redundant with the lower order terms in the model.
>
> Is it then appropriate to remove the lower order interactions from the model (even though they appear significant when I run anova() and given their betas)? I believe I should not be theoretically interpreting time3:A when there is a time3:A:B interaction, anyway.
>
> So, I would interpret the betas for these terms very generally:
> time3:A1:B0 -- The effect of the cubic polynomial modulated by A (1 > 0) when B is held constant at 0.
> time3:A1:B1 -- The effect of the cubic polynomial as modulated by A (1>0) when B is held constant at 1.
>
> Thanks again for your input-- I wouldn't have thought of this is you hadn't mentioned looking at the lower order terms.
>
>
>
> On Fri, Jan 6, 2012 at 1:55 PM, Stefanie Kuchinsky <stefanie.kuchinsky at gmail.com> wrote:
>>
>> Thanks so much for your response. I had not included some of the output table to save space in the original email, but the model does include the lower order terms. I've pasted the full table at the bottom of this email. The polynomial terms were indeed created with the poly() function.
>>
>> You were exactly right about the continuous vs. factor error in my second dataset. I had a typo in my code and so B had never been converted to a factor. I really appreciate you catching that!
>>
>> However, I'm still confused about the interpretation of time4:A1:B1-- specifically why there is no beta for time4:A1:B0 when there is both a beta for time3:A1:B1 and time3:A1:B0?
>>
>>
>> Again, snippet of dataset 1 output:
>>
>> time3:A1:B1 -68.6999 33.14614 9294 -2.07264 0.0382
>> time4:A1:B0 132.5765 23.43786 9294 5.65651 0.0000
>> time4:A1:B1 -124.2845 23.43786 9294 -5.30272 0.0000
>>
>> Corrected output for dataset 2:
>> time3:A1:B1 135.0679 46.2636 9294 2.91953 0.0035
>> time4:A1:B0 80.8813 32.7133 9294 2.47243 0.0134
>> time4:A1:B1 -108.9340 32.7133 9294 -3.32996 0.0009
>>
>>
>> Full table for dataset 1(minus the correlation tables):
>>
>> > summary(m.int4e)
>> Linear mixed-effects model fit by maximum likelihood
>> Data: Data
>> AIC BIC logLik
>> 109842.6 110837.5 -54782.28
>>
>> Random effects:
>> Formula: ~time1 | subjAB
>> Structure: General positive-definite, Log-Cholesky parametrization
>> StdDev Corr
>> (Intercept) 38.33670 (Intr)
>> time1 434.94747 0.488
>> Residual 75.40533
>>
>> Fixed effects: pupil1000 ~ time1 + time2 + time3 + time4 + time5 + subj + subj:time1 + subj:time2 + subj:time3 + subj:time4 + subj:time5 + A:time1 + A:time2 + A:time3 + A:time5 + B:time3 + B:time4 + A:B:time3 + A:B:time4
>> Value Std.Error DF t-value p-value
>> (Intercept) 976.6327 19.63384 9294 49.74231 0.0000
>> time1 891.8779 226.37671 9294 3.93980 0.0001
>> time2 -917.0701 38.86729 9294 -23.59491 0.0000
>> time3 -131.3754 40.59556 9294 -3.23620 0.0012
>> time4 459.9003 40.59556 9294 11.32883 0.0000
>> time5 -444.2458 38.86729 9294 -11.42981 0.0000
>> subj2 47.7965 27.76645 63 1.72137 0.0901
>> subj3 65.4712 27.76645 63 2.35793 0.0215
>> subj4 130.2721 27.76645 63 4.69171 0.0000
>> subj5 57.2987 27.76645 63 2.06359 0.0432
>> subj6 25.6571 27.76645 63 0.92403 0.3590
>> subj7 -7.6969 27.76645 63 -0.27720 0.7825
>> subj8 81.3031 27.76645 63 2.92811 0.0047
>> subj9 15.1726 27.76645 63 0.54644 0.5867
>> subj10 62.5996 27.76645 63 2.25450 0.0276
>> subj11 -64.4270 27.76645 63 -2.32032 0.0236
>> subj12 10.0465 27.76645 63 0.36182 0.7187
>> subj13 43.7500 27.76645 63 1.57564 0.1201
>> subj14 26.4845 27.76645 63 0.95383 0.3438
>> subj15 -46.7323 27.76645 63 -1.68305 0.0973
>> subj16 137.6261 27.76645 63 4.95656 0.0000
>> subj17 14.9735 27.76645 63 0.53926 0.5916
>> subj18 26.3230 27.76645 63 0.94802 0.3467
>> subj19 55.4912 27.76645 63 1.99850 0.0500
>> subj20 98.4027 27.76645 63 3.54394 0.0007
>> subj21 162.8186 27.76645 63 5.86386 0.0000
>> time1:subj2 -848.2627 314.38569 9294 -2.69816 0.0070
>> time1:subj3 -462.8857 314.38569 9294 -1.47235 0.1410
>> time1:subj4 -286.9459 314.38569 9294 -0.91272 0.3614
>> time1:subj5 -350.9655 314.38569 9294 -1.11635 0.2643
>> time1:subj6 -1079.1256 314.38569 9294 -3.43249 0.0006
>> time1:subj7 -958.1396 314.38569 9294 -3.04766 0.0023
>> time1:subj8 396.6793 314.38569 9294 1.26176 0.2071
>> time1:subj9 870.7418 314.38569 9294 2.76966 0.0056
>> time1:subj10 2433.2401 314.38569 9294 7.73967 0.0000
>> time1:subj11 518.0574 314.38569 9294 1.64784 0.0994
>> time1:subj12 -544.9605 314.38569 9294 -1.73341 0.0831
>> time1:subj13 -142.6669 314.38569 9294 -0.45380 0.6500
>> time1:subj14 -447.2835 314.38569 9294 -1.42272 0.1549
>> time1:subj15 73.0371 314.38569 9294 0.23232 0.8163
>> time1:subj16 -147.8436 314.38569 9294 -0.47026 0.6382
>> time1:subj17 -321.5527 314.38569 9294 -1.02280 0.3064
>> time1:subj18 -1104.0885 314.38569 9294 -3.51189 0.0004
>> time1:subj19 -500.0802 314.38569 9294 -1.59066 0.1117
>> time1:subj20 73.0061 314.38569 9294 0.23222 0.8164
>> time1:subj21 -977.4932 314.38569 9294 -3.10922 0.0019
>> time2:subj2 103.9564 53.70288 9294 1.93577 0.0529
>> time2:subj3 462.7823 53.70288 9294 8.61746 0.0000
>> time2:subj4 133.1718 53.70288 9294 2.47979 0.0132
>> time2:subj5 435.4522 53.70288 9294 8.10854 0.0000
>> time2:subj6 866.3608 53.70288 9294 16.13248 0.0000
>> time2:subj7 1040.2131 53.70288 9294 19.36978 0.0000
>> time2:subj8 -48.0412 53.70288 9294 -0.89457 0.3710
>> time2:subj9 -33.9246 53.70288 9294 -0.63171 0.5276
>> time2:subj10 575.5907 53.70288 9294 10.71806 0.0000
>> time2:subj11 -534.9280 53.70288 9294 -9.96088 0.0000
>> time2:subj12 180.5477 53.70288 9294 3.36197 0.0008
>> time2:subj13 -919.1235 53.70288 9294 -17.11498 0.0000
>> time2:subj14 585.8640 53.70288 9294 10.90936 0.0000
>> time2:subj15 405.6596 53.70288 9294 7.55378 0.0000
>> time2:subj16 -1104.0865 53.70288 9294 -20.55917 0.0000
>> time2:subj17 877.9724 53.70288 9294 16.34870 0.0000
>> time2:subj18 1828.7923 53.70288 9294 34.05389 0.0000
>> time2:subj19 820.0829 53.70288 9294 15.27074 0.0000
>> time2:subj20 44.1932 53.70288 9294 0.82292 0.4106
>> time2:subj21 845.2039 53.70288 9294 15.73852 0.0000
>> time3:subj2 658.7997 53.70288 9294 12.26749 0.0000
>> time3:subj3 30.3625 53.70288 9294 0.56538 0.5718
>> time3:subj4 595.8939 53.70288 9294 11.09612 0.0000
>> time3:subj5 243.5716 53.70288 9294 4.53554 0.0000
>> time3:subj6 350.5870 53.70288 9294 6.52827 0.0000
>> time3:subj7 62.7208 53.70288 9294 1.16792 0.2429
>> time3:subj8 187.1384 53.70288 9294 3.48470 0.0005
>> time3:subj9 -745.5636 53.70288 9294 -13.88312 0.0000
>> time3:subj10 -937.4916 53.70288 9294 -17.45701 0.0000
>> time3:subj11 349.5809 53.70288 9294 6.50954 0.0000
>> time3:subj12 -419.0377 53.70288 9294 -7.80289 0.0000
>> time3:subj13 812.8245 53.70288 9294 15.13558 0.0000
>> time3:subj14 179.8396 53.70288 9294 3.34879 0.0008
>> time3:subj15 -150.8652 53.70288 9294 -2.80926 0.0050
>> time3:subj16 1267.6097 53.70288 9294 23.60413 0.0000
>> time3:subj17 223.1138 53.70288 9294 4.15460 0.0000
>> time3:subj18 83.5245 53.70288 9294 1.55531 0.1199
>> time3:subj19 1295.0211 53.70288 9294 24.11455 0.0000
>> time3:subj20 599.0144 53.70288 9294 11.15423 0.0000
>> time3:subj21 142.3725 53.70288 9294 2.65111 0.0080
>> time4:subj2 -357.4785 53.70288 9294 -6.65660 0.0000
>> time4:subj3 -343.2897 53.70288 9294 -6.39239 0.0000
>> time4:subj4 -705.7852 53.70288 9294 -13.14241 0.0000
>> time4:subj5 -445.1367 53.70288 9294 -8.28888 0.0000
>> time4:subj6 -602.6113 53.70288 9294 -11.22121 0.0000
>> time4:subj7 -421.4880 53.70288 9294 -7.84852 0.0000
>> time4:subj8 30.3527 53.70288 9294 0.56520 0.5720
>> time4:subj9 563.3041 53.70288 9294 10.48927 0.0000
>> time4:subj10 -206.4712 53.70288 9294 -3.84470 0.0001
>> time4:subj11 515.5052 53.70288 9294 9.59921 0.0000
>> time4:subj12 184.6193 53.70288 9294 3.43779 0.0006
>> time4:subj13 293.2901 53.70288 9294 5.46135 0.0000
>> time4:subj14 -478.9555 53.70288 9294 -8.91862 0.0000
>> time4:subj15 -240.5382 53.70288 9294 -4.47906 0.0000
>> time4:subj16 -975.5266 53.70288 9294 -18.16526 0.0000
>> time4:subj17 -403.4663 53.70288 9294 -7.51294 0.0000
>> time4:subj18 -876.2704 53.70288 9294 -16.31701 0.0000
>> time4:subj19 -1979.2893 53.70288 9294 -36.85629 0.0000
>> time4:subj20 -534.4526 53.70288 9294 -9.95203 0.0000
>> time4:subj21 -448.4306 53.70288 9294 -8.35022 0.0000
>> time5:subj2 -10.8598 53.70288 9294 -0.20222 0.8397
>> time5:subj3 356.3984 53.70288 9294 6.63649 0.0000
>> time5:subj4 321.0171 53.70288 9294 5.97765 0.0000
>> time5:subj5 159.0899 53.70288 9294 2.96241 0.0031
>> time5:subj6 277.8362 53.70288 9294 5.17358 0.0000
>> time5:subj7 392.0390 53.70288 9294 7.30015 0.0000
>> time5:subj8 76.0262 53.70288 9294 1.41568 0.1569
>> time5:subj9 675.6410 53.70288 9294 12.58109 0.0000
>> time5:subj10 739.3099 53.70288 9294 13.76667 0.0000
>> time5:subj11 -218.8505 53.70288 9294 -4.07521 0.0000
>> time5:subj12 315.8796 53.70288 9294 5.88199 0.0000
>> time5:subj13 -248.9957 53.70288 9294 -4.63654 0.0000
>> time5:subj14 396.2154 53.70288 9294 7.37792 0.0000
>> time5:subj15 231.0236 53.70288 9294 4.30188 0.0000
>> time5:subj16 224.9218 53.70288 9294 4.18826 0.0000
>> time5:subj17 209.4774 53.70288 9294 3.90067 0.0001
>> time5:subj18 505.3070 53.70288 9294 9.40931 0.0000
>> time5:subj19 369.0887 53.70288 9294 6.87279 0.0000
>> time5:subj20 275.5678 53.70288 9294 5.13134 0.0000
>> time5:subj21 480.7268 53.70288 9294 8.95160 0.0000
>>
>>
>> time1:A1 353.1338 85.49229 9294 4.13059 0.0000
>> time2:A1 -68.5389 16.57307 9294 -4.13556 0.0000
>> time3:A1 -154.4407 23.43786 9294 -6.58937 0.0000
>> time5:A1 123.8607 16.57307 9294 7.47361 0.0000
>> time3:B1 100.1996 23.43786 9294 4.27512 0.0000
>> time4:B1 201.6411 23.43786 9294 8.60322 0.0000
>> time3:A1:B1 -68.6999 33.14614 9294 -2.07264 0.0382
>> time4:A1:B0 132.5765 23.43786 9294 5.65651 0.0000
>> time4:A1:B1 -124.2845 23.43786 9294 -5.30272 0.0000
>>
>>
>>
>>
>>
>> On Fri, Jan 6, 2012 at 1:08 PM, Szymek Drobniak <geralttee at gmail.com> wrote:
>>>
>>> Hi,
>>>
>>> for me it's unclear how you specify your data and your model. in general - it seems that you're using user-made polynomial terms? or have you used the poly() function to form them? I'm asking because you don't have most of the lower-order terms in your output. as for the interaction - it's interpretation is fairly straightforward. E.g. interaction of time4:A1:B1 contains the fourth order coefficient of regression for your relationship in the objects from both A1 and B1 groups. The lack of 0/1 next to B in the second example may be caused by accidental conversion of B into numerical (rather than factor) variable - in such a situation it would be treated as continous variable and just a single regression coefficient would be returned.
>>>
>>> cheers,
>>> sz.
>>>
>>> --
>>> Szymon Drobniak || Population Ecology Group
>>> Institute of Environmental Sciences, Jagiellonian University
>>> ul. Gronostajowa 7, 30-387 Kraków, POLAND
>>> tel.: +48 12 664 51 79 fax: +48 12 664 69 12
>>>
>>> www.eko.uj.edu.pl/drobniak
>>
>>
>
--
Szymon Drobniak || Population Ecology Group
Institute of Environmental Sciences, Jagiellonian University
ul. Gronostajowa 7, 30-387 Kraków, POLAND
tel.: +48 12 664 51 79 fax: +48 12 664 69 12
www.eko.uj.edu.pl/drobniak
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