[R] Re: comparing predicted sequence A'(t) to observed sequence A(t)

[Spencer Graves]

      Regarding applying repeated measures to time series, the lme 
software in packages nlme and lme4 provide many options for doing that.  
The best discussion I know of this is Pinheiro and Bates (2000) 
Mixed-Effects Models in S and S-PLUS (Springer). 

      hope this helps.  spencer graves

Christian Jost wrote:

>> From: Suresh Krishna <ssk2031 at columbia.edu>
>> Subject: [R] comparing predicted sequence A'(t) to observed sequence
>>     A(t)
>> To: r-help at stat.math.ethz.ch
>> Message-ID: <420DE463.8080009 at columbia.edu>
>> Content-Type: text/plain; charset=ISO-8859-1; format=flowed
>>
>>
>> Hi,
>>
>> I have a question that I have not been succesful in finding a definitive
>> answer to; and I was hoping someone here could give me some pointers to
>> the right place in the literature.
>>
>> A. We have 4 sets of data, A(t), B(t), C(t), and D(t). Each of these
>> consists of a series of counts obtained in sequential time-intervals: so
>>   for example, A(t) would be something like:
>>
>> Count A(t):  25,    28,    26,   34   ......
>> Time (ms):  0-10, 10-20, 20-30, 30-40 .......
>>
>> Each count in the series A(t) is obtained by summing the total number of
>> observed counts over multiple (say 50), independent repetitions of that
>> time-series. These counts are generally known to be Poisson distributed,
>> and the 4 processes A(t), B(t), C(t) and D(t) are independent of each 
>> other.
>>
>> B. It appears on visual observation that the following relationship
>> holds; and such a relationship would also be expected on mechanistic
>> considerations.
>>
>> A(t) = B(t) + C(t) - D(t)
>>
>> We now want to test this hypothesis statistically.
>>
>> Because successive counts in the sequence are likely to be correlated,
>> isnt it true that none of these methods are valid ? Perhaps for other
>> reasons as well ?
>>
>> a)Doing a chi-squared test to see if the predicted curve for A(t)
>> deviates significantly from the observed A(t); this also seems to not
>> take the variability of the predicted curve into account.
>>
>> b)Doing a regression of the predicted values of A(t) against the actual
>> values of A(t) and checking for deviations of slope from 1 and intercept
>> from 0 ? Here, in addition to lack of independence, the fact that
>> X-values are not fixed (i.e. are variable) and the fact that X and Y are
>> Poisson distributed counts should also be taken into account, right ?
>>
>> I would be very grateful if someone could point me to methods to handle
>> this kind of situation, or where to look for them. Is there something in
>> the time-series literature, for instance ?
>>
>>
>
> This is a frequent problem I also encounter when wanting to compare 
> two dynamic processes (e.g. temporal evolution of number of ants on 
> two branches). To my knowledge there is no general statistical way to 
> compare these two time series. But in your case you might try a 
> repeated measure anova, e.g. to compare A(t) against B(t)+C(t)-D(t), 
> put in a first column 'counts' the counts for A and then for B+C-D, in 
> a second column 'time' the correspoding t, in a third column 'series' 
> mark the A measures by "A" and the B+C-D measures by "BCD", then run 
> an anova
> summary(aov(counts ~ series:time + Error(series)))
>
> This works if there are replicates of conditions "A" and "BDC", but I 
> am not a statistitian and am not sure whether it applies to your case 
> (though, you seem to have repetitions, so you might use this 
> information instead of only looking at the sums).
> For a hands-on example with behavioural data of mice (with or without 
> treatment, 4 training session for each mouse, does treatment affect 
> training) see
> http://cognition.ups-tlse.fr/_christian/M7P14M/TP7/TP-Anova.pdf
> with the data in
> http://cognition.ups-tlse.fr/_christian/M7P14M/TP7/tp-anova.rda
> (well, its in french, but the R formulas should be understandable ;-)
>
> Well, as I said, I am not a statistitian, there might be a logical 
> flaw in applying repeated measures anova to time series, if anybody 
> out there sees one please tell us ;-)
>
> Best, Christian.