R help - Aug 2006 - Type II and III sum of square in Anova (R, car package)

Hello everybody,

I have some questions on ANOVA in general and on ANOVA in R particularly.
I am not Statistician, therefore I would be very appreciated if you answer
it in a simple way.

1. First of all, more general question. Standard anova() function for lm()
or aov() models in R implements Type I sum of squares (sequential), which
is not well suited for unbalanced ANOVA. Therefore it is better to use
Anova() function from car package, which was programmed by John Fox to use
Type II and Type III sum of squares. Did I get the point?

2. Now more specific question. Type II sum of squares is not well suited
for unbalanced ANOVA designs too (as stated in STATISTICA help), therefore
the general rule of thumb is to use Anova() function using Type II SS
only for balanced ANOVA and Anova() function using Type III SS for
unbalanced ANOVA? Is this correct interpretation?

3. I have found a post from John Fox in which he wrote that Type III SS
could be misleading in case someone use some contrasts. What is this about?
Could you please advice, when it is appropriate to use Type II and when
Type III SS? I do not use contrasts for comparisons, just general ANOVA
with subsequent Tukey post-hoc comparisons.

Thank you in advance,
Amasco

	[[alternative HTML version deleted]]

> 1. First of all, more general question. Standard anova() function for lm()
> or aov() models in R implements Type I sum of squares (sequential), which
> is not well suited for unbalanced ANOVA. Therefore it is better to use
> Anova() function from car package, which was programmed by John Fox to use
> Type II and Type III sum of squares. Did I get the point?
> 
> 2. Now more specific question. Type II sum of squares is not well suited
> for unbalanced ANOVA designs too (as stated in STATISTICA help), therefore
> the general rule of thumb is to use Anova() function using Type II SS
> only for balanced ANOVA and Anova() function using Type III SS for
> unbalanced ANOVA? Is this correct interpretation?
> 
> 3. I have found a post from John Fox in which he wrote that Type III SS
> could be misleading in case someone use some contrasts. What is this about?
> Could you please advice, when it is appropriate to use Type II and when
> Type III SS? I do not use contrasts for comparisons, just general ANOVA
> with subsequent Tukey post-hoc comparisons.
 
There are many threads on this list that discuss this issue. Not being a great
statistician myself, I would suggest you read through some of these as a start.
As I understand, the best philosophy with regards to types of sums of squares is
to use the type that tests the hypothesis you want. They were developed as a
convenience to test many of the hypotheses a person might want
"automatically,"
and put it into a nice, neat little table. However, with an interactive system
like R it is usually even easier to test a full model vs. a reduced model. That
is if I want to test the significance of an interaction, I would use
anova(lm.fit2, lm.fit1) where lm.fit2 contains the interaction and lm.fit2 does
not. The anova function will return the appropriate F-test. The danger with
worrying about what type of sums of squares to use is that often we do not think
about what hypotheses we are testing and if those hypotheses make sense in our
situation.

Mark Lyman

I think this starts from the position of a batch-oriented package.
In R you can refit models with update(), add1() and drop1(), and 
experienced S/R users almost never use ANOVA tables for unbalanced 
designs.  Rather than fit a pre-specified set of sub-models, why not fit 
those sub-models that appear to make some sense for your problem and data?

SInce your post lacks a signature and your credentials we have no idea of 
your background, which makes it very difficult even to know what reading 
to suggest to you.  But Bill Venables' 'exegeses' paper 
(http://www.stats.ox.ac.uk/pub/MASS3/Exegeses.pdf) may be a good start.
It does explain your comment '3.'.

On Sun, 27 Aug 2006, Amasco Miralisus wrote:
> Hello everybody,
> 
> I have some questions on ANOVA in general and on ANOVA in R particularly.
> I am not Statistician, therefore I would be very appreciated if you answer
> it in a simple way.
> 
> 1. First of all, more general question. Standard anova() function for lm()
> or aov() models in R implements Type I sum of squares (sequential), which
> is not well suited for unbalanced ANOVA. Therefore it is better to use
> Anova() function from car package, which was programmed by John Fox to use
> Type II and Type III sum of squares. Did I get the point?
> 
> 2. Now more specific question. Type II sum of squares is not well suited
> for unbalanced ANOVA designs too (as stated in STATISTICA help), therefore
> the general rule of thumb is to use Anova() function using Type II SS
> only for balanced ANOVA and Anova() function using Type III SS for
> unbalanced ANOVA? Is this correct interpretation?
> 
> 3. I have found a post from John Fox in which he wrote that Type III SS
> could be misleading in case someone use some contrasts. What is this about?
> Could you please advice, when it is appropriate to use Type II and when
> Type III SS? I do not use contrasts for comparisons, just general ANOVA
> with subsequent Tukey post-hoc comparisons.
> 
> Thank you in advance,
> Amasco
> 
> 	[[alternative HTML version deleted]]
> 
> ______________________________________________
> R-help at stat.math.ethz.ch mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
> 
-- 
Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272866 (PA)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595

Dear Amasco,

A complete explanation of the issues that you raise is awkward in an email,
so I'll address your questions briefly. Section 8.2 of my text, Applied
Regression Analysis, Linear Models, and Related Methods (Sage, 1997) has a
detailed discussion.

(1) In balanced designs, so-called "Type I," "II," and
"III" sums of squares
are identical. If the STATA manual says that Type II tests are only
appropriate in balanced designs, then that doesn't make a whole lot of sense
(unless one believes that Type-II tests are nonsense, which is not the
case).

(2) One should concentrate not directly on different "types" of sums
of
squares, but on the hypotheses to be tested. Sums of squares and F-tests
should follow from the hypotheses. Type-II and Type-III tests (if the latter
are properly formulated) test hypotheses that are reasonably construed as
tests of main effects and interactions in unbalanced designs. In unbalanced
designs, Type-I sums of squares usually test hypotheses of interest only by
accident. 

(3) Type-II sums of squares are constructed obeying the principle of
marginality, so the kinds of contrasts employed to represent factors are
irrelevant to the sums of squares produced. You get the same answer for any
full set of contrasts for each factor. In general, the hypotheses tested
assume that terms to which a particular term is marginal are zero. So, for
example, in a three-way ANOVA with factors A, B, and C, the Type-II test for
the AB interaction assumes that the ABC interaction is absent, and the test
for the A main effect assumes that the ABC, AB, and AC interaction are
absent (but not necessarily the BC interaction, since the A main effect is
not marginal to this term). A general justification is that we're usually
not interested, e.g., in a main effect that's marginal to a nonzero
interaction.

(4) Type-III tests do not assume that terms higher-order to the term in
question are zero. For example, in a two-way design with factors A and B,
the type-III test for the A main effect tests whether the population
marginal means at the levels of A (i.e., averaged across the levels of B)
are the same. One can test this hypothesis whether or not A and B interact,
since the marginal means can be formed whether or not the profiles of means
for A within levels of B are parallel. Whether the hypothesis is of interest
in the presence of interaction is another matter, however. To compute
Type-III tests using incremental F-tests, one needs contrasts that are
orthogonal in the row-basis of the model matrix. In R, this means, e.g.,
using contr.sum, contr.helmert, or contr.poly (all of which will give you
the same SS), but not contr.treatment. Failing to be careful here will
result in testing hypotheses that are not reasonably construed, e.g., as
hypotheses concerning main effects.

(5) The same considerations apply to linear models that include quantitative
predictors -- e.g., ANCOVA. Most software will not automatically produce
sensible Type-III tests, however.

I hope this helps,
 John

--------------------------------
John Fox
Department of Sociology
McMaster University
Hamilton, Ontario
Canada L8S 4M4
905-525-9140x23604
http://socserv.mcmaster.ca/jfox 
-------------------------------- 
> -----Original Message-----
> From: r-help-bounces at stat.math.ethz.ch 
> [mailto:r-help-bounces at stat.math.ethz.ch] On Behalf Of Amasco 
> Miralisus
> Sent: Saturday, August 26, 2006 5:07 PM
> To: r-help at stat.math.ethz.ch
> Subject: [R] Type II and III sum of square in Anova (R, car package)
> 
> Hello everybody,
> 
> I have some questions on ANOVA in general and on ANOVA in R 
> particularly.
> I am not Statistician, therefore I would be very appreciated 
> if you answer it in a simple way.
> 
> 1. First of all, more general question. Standard anova() 
> function for lm() or aov() models in R implements Type I sum 
> of squares (sequential), which is not well suited for 
> unbalanced ANOVA. Therefore it is better to use
> Anova() function from car package, which was programmed by 
> John Fox to use Type II and Type III sum of squares. Did I 
> get the point?
> 
> 2. Now more specific question. Type II sum of squares is not 
> well suited for unbalanced ANOVA designs too (as stated in 
> STATISTICA help), therefore the general rule of thumb is to 
> use Anova() function using Type II SS only for balanced ANOVA 
> and Anova() function using Type III SS for unbalanced ANOVA? 
> Is this correct interpretation?
> 
> 3. I have found a post from John Fox in which he wrote that 
> Type III SS could be misleading in case someone use some 
> contrasts. What is this about?
> Could you please advice, when it is appropriate to use Type 
> II and when Type III SS? I do not use contrasts for 
> comparisons, just general ANOVA with subsequent Tukey 
> post-hoc comparisons.
> 
> Thank you in advance,
> Amasco
> 
> 	[[alternative HTML version deleted]]
> 
> ______________________________________________
> R-help at stat.math.ethz.ch mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide 
> http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.

I cannot resist a very brief entry into this old and seemingly
immortal issue, but I will be very brief, I promise!

Amasco Miralisus suggests:
> As I understood form R FAQ, there is disagreement among Statisticians
> which SS to use
>
(http://cran.r-project.org/doc/FAQ/R-FAQ.html#Why-does-the-output-from-a
nova_0028_0029-depend-on-the-order-of-factors-in-the-model_003f).

To let this go is to concede way too much.  The 'disagreement' is
really over whether this is a sensible question to ask in the first
place.  One side of the debate suggests that the real question is what
hypotheses does it make sense to test and within what outer
hypotheses.  Settle that question and no issue on "types" of sums of
squares arises.

This is often a hard question to get your head around, and the
attraction of offering a variety of 'types of sums of squares' holds
out the false hope that perhaps you don't need to do so.  The bad
news is that for good science and good decision making, you do.

Bill Venables.

Short story: January 2006 I did some analysis in R-2.2.1 using nls. Repeating
the exercise in R-2.3.1 yesterday produced somewhat different results.

After some debugging I found that either nls is the problem or that mine
understanding of environments or scoping rules is lacking something.

This is a short reproducing example.



x <- seq(0,5,len=20)

n <- 1
y <- 2*x^2 + n + rnorm(x)

xy <- data.frame(x=x,y=y)

myf <- function(x,a,b,n){
  res <- a*x^b + n
  ## a print for debugging purpose
  print(n)
  res
}

## This works as I expect it to do in R-2.2.1 but doesn't work in R-2.3.1. 
## n is somehow sat to nrow(xy) inside nls()
## Note that x and y is defined in the dataframe xy, whereas n is found in the
global environment.
fit <- nls(y ~ myf(x,a,b,n), data=xy, start=c(a=1,b=1), trace=TRUE)

## this works in both versions
## x,y,n found in the .GlobalEnv
fit <- nls(y ~ myf(x,a,b,n), start=c(a=1,b=1), trace=TRUE)

## this works in both versions.
## x, y, n found in dataframe xyn
xyn <- data.frame(xy,n=n)
fit <- nls(y ~ myf(x,a,b,n), data=xyn, start=c(a=1,b=1), trace=TRUE)

## this works in both versions
## Now using the variable .n instead of n
## .n is found in .GlobaEnv
.n <- 1
fit <- nls(y ~ myf(x,a,b,.n), data=xy, start=c(a=1,b=1), trace=TRUE)


In my real case and the example above, I do have three or more parameters of
which fitting is done only on few of theme. Is this a problem? Or should I ask,
why is this a problem in R-2.3.1 but not in R-2.2.1?

Is my problem related to this difference between lines of code from nls:

R-2.2.1:     mf <- as.list(eval(mf, parent.frame()))

R-2.3.1:     mf <- eval.parent(mf)
             n <- nrow(mf)
             mf <- as.list(mf)

where n is being defined in the scope of nls in the latest version?

Best regards

Frede Aakmann T?gersen



Danish Institute of Agricultural Sciences
Research Centre Foulum
Dept. of Genetics and Biotechnology
Blichers All? 20, P.O. BOX 50
DK-8830 Tjele

Phone:   +45 8999 1900
Direct:  +45 8999 1878

E-mail:  FredeA.Togersen at agrsci.dk
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