Phillip Alday

2017-Dec-01 10:11 UTC

### [R] How to extract coefficients from sequential (type 1), ANOVAs using lmer and lme

Please reread my point #1: the tests of the (individual) coefficients in the model summary are not the same as the ANOVA tests. There is a certain correspondence between the two (i.e. between the coding of your categorical variables and the type of sum of squares; and for a model with a single predictor, F=t^2), but they are not the same in general. The t-test in the model coefficients is simply the ratio of the estimate to the standard error (i.e. a Wald test), and the standard errors, like the estimates, are all calculated at the same time. So in that sense, the t-tests are always marginal (cf. Pinheiro and Bates 2000, pp. 90-91). I would also encourage you to focus more on your estimates (the Value column) and less on p-values. All that said, it seems you only care about the significance of model terms and not the estimates, so there are two possibilities for sequential tests: 1. Nested model comparison (likelihood-ratio test) with either the anova() function or drop1(model,test='Chisq') 2. use the p-values from the ANOVA results (see Pinheiro and Bates 2000, pp. 90-91, for some notes on which test is preferred as well as the GLMM FAQ: https://bbolker.github.io/mixedmodels-misc/glmmFAQ.html) But please please note that it would be misleading to say that these are the p-values for the coefficients in your model. These issues are the same for both mixed and 'normal' regression models. Phillip On 30/11/17 16:56, Akihiro Koyama wrote:> Hi Phillip, > > Thank you very much for informative comments. But I still cannot find a > way to extract coefficients from sequential ANOVAs. > > I have many data sets which all give different p-values for "sequential" > and "marginal" options in anova(). But summary() command looks only > provide me coefficients associated with "marginal" ANOVAs. > > > > > On Tuesday, November 28, 2017 6:51 AM, Phillip Alday > <phillip.alday at mpi.nl> wrote: > > > Be careful when mixing lme4 and lmerTest together -- lmerTest extends > and changes the behavior of various lme4 functions. > > From the help page for lme4-anova (?lme4::anova.merMod) > >> ?anova?: returns the sequential decomposition of the contributions >> of fixed-effects terms or, for multiple arguments, model >> comparison statistics. For objects of class ?lmerMod? the >> default behavior is to refit the models with ML if fitted >> with ?REML = TRUE?, this can be controlled via the ?refit? >> argument. See also ?anova?. > > So lme4-anova will give you sequential tests; note, however, that lme4 > won't calculate the denominator degrees of freedom for you and thus > won't give p-values. See the FAQ > (https://cran.r-project.org/doc/FAQ/R-FAQ.html#Why-are-p_002dvalues-not-displayed-when-using-lmer_0028_0029_003f) > > From the help page for lmerTest-anova (?lmerTest::anova.merModLmerTest): >> Usage: >> >> ## S4 method for signature 'merModLmerTest' >> anova(object, ... , ddf="Satterthwaite", >> type=3) >> >> Arguments: >> > ... >> type: type of hypothesis to be tested. Could be type=3 or type=2 or >> type = 1 (The definition comes from SAS theory) > > > So lmerTest-anova by default gives you Type III ('marginal', although > Type II is what actually gives you tests that respect the Principle of > Marginality; see John Fox's Applied Regression Analysis (book) or > Venables' "Exegeses on Linear Models" > (https://www.stats.ox.ac.uk/pub/MASS3/Exegeses.pdf) for more information > on that. Type I tests are the sequential tests, so with anova(model, > type=1), you will get the sequential tests you want. lmerTest will > approximate the denominator degrees of freedom for you (using > Satterthwaite method by default, or the more computationally intensive > Kenward-Roger method), so you'll get p-values if that's what you want. > > Finally, it's important to note two things: > > 1. The "type"-argument for nlme::summary doesn't actually do anything > (see ?nlme::summary.lme). It's just passed onto the 'print' method, > where it's silently ignored. The 'type' of sum of squares is an > ANOVA-thing; the closest correspondence in terms of model coefficients > is the coding of your categorical contrasts. See the literature > mentioned above for more details as well as Dale Barr's discussion on > simple vs. main effects in regression models > (http://talklab.psy.gla.ac.uk/tvw/catpred/). > > (?nlme::anova.lme does have indeed have a 'type' argument.) > > 2. It is possible for the sequential tests and the marginal tests to > yield the same results. Again, see the above literature. You have no > interactions in your model and continuous (i.e. not-categorical) > predictors, so if they're orthogonal, then the sequential and marginal > tests will be numerically the same, even if they test different > hypotheses. (See section 5.2, starting on page 14; the sequential tests > are the "eliminating" tests, while the marginal tests are the "ignoring" > tests in that explanation.) > > Best, > Phillip > > > On 28/11/17 12:00, r-help-request at r-project.org > <mailto:r-help-request at r-project.org> wrote: >> I wantto run sequential ANOVAs (i.e. type I sums of squares), and > trying to getresults including ANOVA tables and associated coefficients > for predictive variables(I am using the R 3.4.2 version). I think ANOVA > tables look right, but believecoefficients are wrong. Specifically, it > looks like that the coefficients arefrom ANOVA with ?marginal? (type III > sums of squares). I have tried both lme (nlmepackage) and lmer (lme4 + > lmerTEST packages). Examples of the results arebelow: >> > > > <snip> > > >> Ibelieve the results from summary() are for ?marginal? instead of > ?sequential?ANOVA because the p-value (i.e., 0.237 for narea) in summary > are identical tothose in tables from ?marginal?. I also used lmer in the > lme4 pacakge to findthe same results (summary() results look like from > ?marginal?). >> >> >> Cananybody tell me how to get coefficients for ?sequential? ANOVAs? > Thank you. >> > > >