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

> <

[hidden email]> 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,

[hidden email]
> <mailto:

[hidden email]> 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.

>>

>

>

>

______________________________________________

[hidden email] mailing list -- To UNSUBSCRIBE and more, see

https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide

http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code.