Dear list,

Emmanuel, thank you for your long answer.

See below,

2010/3/27 Christophe Dutang <dutangc@gmail.com>

> Some additions to what I wrote yesterday : I misunderstood the aim of the
> paper as explained in its abstract, and started too far ...
>
> Okay. I have been able to lay my eyes on this article. The point it makes
> is that the "mixed model" approach to analysing repeated measurements on the
> same subject allows you to use observations made on this subject having
> complete *data*, discarding only the *observations* with *missing* *data*,
> whereas the old "repeated measures ANOVA" would lead you to ignore *all*
> observations made on a *subject* having *one* observation with *missing* *
> data*.
>
> This is due to the fact that what the article calls the "repeated measures
> ANOVA" algorithms were (geometrically very smart) *manually* computable
> simplifications of a more general procedure involving, in the general case,
> manually intractable computation (multiple matrix inversions of not-so-small
> dimensions) ; these simplifications (and the resulting algorithms) were
> valid only for at least partially *balanced* datasets.
>
> (g)lmer() (and its predecessor lme()) of course allow for this use of *
> data* on incompletely documented *subjects*. This is so obvious to users
> of "modern" software (i. e. using something else than transcriptions of
> manual computation algorithms) that it is no longer mentioned as an issue.
> The situation is similar to 2-way fixed-effects ANOVA, where the "manual"
> algorithm I was taught ... too long a time ago *demanded* a balanced
> datasets, which is a requirement that ended even with BMDP (end of 70's,
> IIRC). Similarly, nowhere I'm aware of the authors of lm() mention that
> multiway-models do not have to be balanced : that's granted...
>
> However, what the authors of that papers of yours do *not* mention is that
> analyzing this incomplete dataset by using all the complete *observations*,
> while better that using only complete *subjects*, might still lead to biased
> estimates, and that debiasing them should involve multiple imputations of
> *missing* *data* in incomplete *observations*. That subject was well
> explored by Rubin (since the 80's IIRC), and involves the specialized
> packages I mentioned yesterday ... or turning to Bayesian estimation, which
> is a horse of an entirely different color. Look up the 2nd edition of
> Rubin's book (ca 1998 IIRC) on the subject for (much) better explanations.
>
> To summarize :
>
> Repeated-measures ANOVA : manually tractable, needs balanced datasets,
> therefore forces you to ignore incomplete *subjects*. Obsolete (but smart an
> historically *important*).
>
Just to be sure to understand what you are talking about. Repeated-measures
ANOVA are modelled by

Y_it = mu + alpha_i + e_it ?


> Mixed-model ANOVA : manually intractable, accepts unbalanced datasets but
> does not allow for partial observations, therefore forces you to ignore
> incomplete *observations*. Modern solution, but does not accounts for
> possible bias due to *missing* *data*.
>
Y_it = Z_it . alpha_i + X_it . beta + e_it

Is that correct? by the way, why we call them ANOVA models? (in my
scolarship, anova was introduced for anova table.)

> ===== Your paper stops here (and I started here yesterday) =====
>
> Multiple imputations + Mixed-model ANOVA : allows you to use all available
> information, estimates the loss of information incurred by *missing* *data
> * and attempts to make up for it. Best frequentist (classical) solution,
> needs specialized software, and might require special modeling efforts of
> the *missing*-*data* mechanism if "*missing* at random" is not "obviously"
> reasonable.
>
Bayesian modeling : requires serious efforts to model both the phenomenon of
> interest, its covariates and possibly the *missing*-*data* mechanism and a
> priori information, needs some awareness of the computational difficulties
> (not always solvable), current tools not yet perfected, but is
> (theoretically) the best possible solution since it attempts to model the
> joint distribution of all *data*, including their missingness. The answers
> it leads to (distributions, credible intervals, Bayes factors,
> probabilities) have intuitive meanings, quite different of "frequentist"
> confidence intervals and p-values, and might not (yet) be accepted in some
> circles insisting, for example, on hypothesis testing.
>
Do you have any good reference on this topic? a good implementation of this
approach is the MCMCpack?

> HTH,
>
> Emmanuel Charpentier
>
> PS : since "manual" algorithms are out of practical use since the end of
> the 70s and the inception of what was then called "personal computers", I'm
> a bit surprised that a paper published in 2004 still invokes that issue...
> Is your domain special (or especially conservative) ?
>
I'm working in actuarial science. But I had just googled the paper and have
no particular link to that domain.


> How about survival analysis with censoring?
>>
>
Looking on wikipedia I found the Cox Model which seems the simplest
regression model. The Introduction of John Fox seems the best introduction
on survival analysis and regression models.

Thanks again

Christophe


>
>>
>> HTH
>>
>>
>> Cheers,
>>
>> Luca
>>
>>
>>
>>
>> ----- Original Message ----- From: "christophe dutang" <dutangc@gmail.com
>> >
>> To: "David Duffy" <David.Duffy@qimr.edu.au>
>> Cc: <r-sig-mixed-models@r-project.org>
>> Sent: Friday, March 26, 2010 1:15 PM
>> Subject: Re: [R-sig-ME] missing data + explanatory variables
>>
>>
>>  Hello,
>>>
>>> 2010/3/26 David Duffy <David.Duffy@qimr.edu.au>
>>>
>>>  On Thu, 25 Mar 2010, Christophe Dutang wrote:
>>>>
>>>> I try to model a binary response variable over a small period of time.
>>>> The
>>>>
>>>>>  problem is that for some lines, the response is missing. In this
>>>>>>> mailing
>>>>>>> list archive, I do not find response to this question.
>>>>>>>
>>>>>>> fm1 <- lmer(Reaction ~ Days + (Days|Subject), sleepstudy)
>>>>>>>
>>>>>> sleepstudy2 <- sleepstudy
>>>>> sleepstudy2[180, "Reaction"] <- NA
>>>>> fm2 <- lmer(Reaction ~ Days + (Days|Subject), sleepstudy2)
>>>>>
>>>>> What am I doing wrong?
>>>>>
>>>>>
>>>> This worked perfectly, did it not?
>>>>
>>>
>>> the observation number is reduced by 1.
>>>
>>>
>>>  As Emmanuel Charpentier summarized, you can't use information from the
>>>> "lines" where the response is missing (expect for prediction, the BLUP)
>>>> unless you move to some type of multivariate model that explicitly
>>>> models
>>>> the interrelationships of the covariates, like the multiple imputation
>>>> models or SEM.
>>>>
>>>
>>> I don't receive anything from E. Charpentier?!
>>>
>>>
>>>  But in that case, all that happens is you gain a little bit of
>>>> information
>>>> about the distributions of the covariates, which may or may not
>>>> influence
>>>> your model for the response variable.
>>>>
>>>>
>>> By "some lines are missing", I mean I don't have both the response and
>>> the
>>> covariate. Let me explain what I'm doing. I work on default of
>>> individual.
>>> Every 6 month for each indvidual the response variable equals to 1 if he
>>> defaults on the period, 0 otherwise. For each time period I also observe
>>> explanatory variables (age, job, marital status,...).
>>>
>>> The problem is that my response is always of this pattern:
>>> 0 0 0 1
>>> 0 0 0 0
>>> 0 1 NA NA
>>> That's wher I had missing data, after the default, I don't have any data
>>> for
>>> that individual. And the variable is necessary a sequence of 0 with a
>>> possible 1 at the end.
>>>
>>> I'm trying to use something better than the logistic GLM at each time
>>> period.
>>>
>>> Thanks in advance for any advice
>>>
>>> Christophe
>>>
>>>
>>>
>>>> PS what are the "lines" you refer to?  What is the actual problem you
>>>> are
>>>> working on?
>>>>
>>>>
>>>> --
>>>> | David Duffy (MBBS PhD)                                         ,-_|\
>>>> | email: davidD@qimr.edu.au  ph: INT+61+7+3362-0217 fax: -0101  /     *
>>>> | Epidemiology Unit, Queensland Institute of Medical Research   \_,-._/
>>>> | 300 Herston Rd, Brisbane, Queensland 4029, Australia  GPG 4D0B994A v
>>>>
>>>>
>>>
>>>
>>> --
>>> Christophe DUTANG
>>> Ph. D. student at ISFA
>>>
>>> [[alternative HTML version deleted]]
>>>
>>> _______________________________________________
>>> R-sig-mixed-models@r-project.org mailing list
>>> https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
>>>
>>
>>
>


-- 
Christophe DUTANG
Ph. D. student at ISFA

	[[alternative HTML version deleted]]


