For example, data consisting of a proportions with:
- Numerator (time required to do something, in seconds) and Denominator (duration of experiment, in seconds)
- Numerator (number of events) and Denominator (duration of experiment, in second)
Dear Giovanni Bubici,
if you would like to analyze the stability of a process, e.g. number of events per experiment, which is a time series it is probably interesting to use an Allan Variance:
This is widely used in the domain of frequency measurements or clock characterization.
http://en.wikipedia.org/wiki/Allan_variance
You can use time series in SAS statistical package if you have access to SAS or any any statistical program which have time series.
I use SAS, but never used time series, that actually sound good! May you provide a simple example of SAS programming including a dataset?
If you are dealing with proportions, you must first transform your data using compositional data analysis techniques. This assures that the analysis does not depend on units, on the definition of the total sum of proportions and that you will not have to interpret proportions greater than 100% or lower than 0%. Then you can freely apply time series techniques across your transformed data. This paper may guide you in the process.
http://dugi-doc.udg.edu/bitstream/handle/10256/723/Bergman_paper.pdf?sequence=1
As for the tools, I suggest the use of R. There are some packages that offer functions to deal with proportions, namely in the "compositions" package. This package is thoroughly described in the book "Analyzing compositional data with R" (Springer). As for time series, R includes some functions, but you might have a look at the "forecast" package.
Estimation of models for multilevel multinomial data or for
time-series data are challenging problems individually; doing both
simultaneously, even more so.
I a multinomial option is not implemented in many multilevel
software packages (e.g., lme4)
I time-series data can have complex dependencies that require
special techniques; approaches that use “regular” standard
errors without accounting for these dependencies are not to
be trusted!
Time is a continuous predictor:
For every unit change in time, make a change in the log odds
of the outcome that is a function of time
Possible functions include:
a) Natural polynomials (Barr, 2008)
b)Orthogonal polynomials (Mirman, Dixon, Magnuson, 2008)
c) Splines
d) Other nonlinear functions (Scheepers, Keller, Lapata, 2007)
Time-locking
Time-locking is the process of defining a time window of data to analyze
by choosing a beginning point and end point.
Issue: Choice of time window can affect results. Need to have a (semi-)
principled way to choose the window.
Heuristics for time-locking:
a) Use knowledge of domain (e.g., no effects on EMs prior to 180-200 ms)
b) Visualize grand mean data (collapsed over conditions)
c) Visualize the data on the scale of the regression (log odds)
d) Avoid fitting asymptotic segments (no change)
e) For self-terminated trials, set end point so that no more than 5-10% of data is
missing
f) Look for “breakpoint” to find onset of stimulus-driven effects
g) Apparent breakpoint @ 200 ms (NB: we will later see that this break is unrelated
to referential processing)
h) Choose end point based on RT (blue line represents prop. of trials that have not
yet terminated)
i) End point @ 783 ms (still have 95% of data)
Choosing a polynomial function
Strategy:
a) Use grand mean data so that model choice is not influenced by condition differences
b) Visualize on the scale of the regression (log odds), log ( p/1−p ).
c) Order of function is equal to number of bends + 1.
- Badges
- Science topic