Message-ID: <CANXb-o6-Wwv9eaGq1ofGxPyODtKFQpLayJJpCVOzBF_QSk6=aw@mail.gmail.com>
Date: 2012-01-06T20:05:38Z
From: Szymek Drobniak
Subject: question regarding summary output with three-way interactions
In-Reply-To: <CABhs0QYvR4yQ87GhozjDAc5ZW6eXbWEEU+PH4-1WMU1r4pf3jg@mail.gmail.com>
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 Krak?w, 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 Krak?w, POLAND
tel.: +48 12 664 51 79 fax: +48 12 664 69 12
www.eko.uj.edu.pl/drobniak