The only differences between MAR and MNAR is that for MNAR you need to 
explicitly model the nonresponse mechanism and you can make infinite 
MNAR assumptions (there is not a definite MNAR analysis). Under ML 
analysis any MAR nonresponse mechanism is ignorable, although under 
frequentist analysis not.

It is important to note that the (saturated) MAR is untestable too. You 
can only test if the MCAR (or other non-saturated MAR/MNAR) assumption 
is plausible conditional another assumed mechanism.

Unfortunately, the uncertainty (mainly the ignorance) provided by the 
missing data do not lead us to have "concrete" proofs... This is why it 
is important to perform sensitivity analysis under a variety of 
assumptions and using a bigger class of models to give intervals of 
ignorance/uncertainty.

Good luck,

Frederico Zanqueta Poleto
fred@poleto.com
--
"An approximate answer to the right problem is worth a good deal more than an exact answer to an approximate problem." J. W. Tukey



Dimitris Rizopoulos wrote:

>This depends on the analysis you want to do; Maximum Likelihood will 
>give you unbiased results even under MAR. In this case the more 
>relevant question is whether the missing data mechanism is MNAR, in 
>which case ML might give you biased results. Unfortunately you cannot 
>test MNAR without making, some times very strong, assumptions.
>
>Best,
>Dimitris
>
>----
>Dimitris Rizopoulos
>Ph.D. Student
>Biostatistical Centre
>School of Public Health
>Catholic University of Leuven
>
>Address: Kapucijnenvoer 35, Leuven, Belgium
>Tel: +32/(0)16/336899
>Fax: +32/(0)16/337015
>Web: http://www.med.kuleuven.be/biostat/
>     http://www.student.kuleuven.be/~m0390867/dimitris.htm
>
>
>----- Original Message ----- 
>From: "Rohit Vishal Kumar" <rohitvk@vsnl.com>
>To: <r-help@stat.math.ethz.ch>
>Sent: Monday, November 14, 2005 5:40 PM
>Subject: [R] Little's Chi Square test for MCAR?
>
>
>  
>
>>Hi.
>>
>>Can anyone point me to any module in R which implements "Little's 
>>Chi
>>Square test" for MCAR.
>>The problem is that i have around 60 behavioural variables on a 6 
>>point
>>categorical scale which i need to test for MCAR and MAR. What i can 
>>make
>>out from preliminary analysis is that moderate (0.30 to 0.60)
>>correlations  may be present in several variable pairs leading me to
>>suspect that the data may not be MCAR or MAR. However i need some 
>>more
>>"concrete" proof.
>>
>>Any help - onlist or offlist - would be greatly appreciated.
>>
>>Thanks in Advance
>>
>>Rohit Vishal Kumar
>>Ph.D. Student (Calcutta) India
>>
>>______________________________________________
>>R-help@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
>>
>>    
>>
>
>
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