R help - Aug 2009 - breaking multi-modal histograms down into combinations of unimodal distributions

Dear All,

Does anybody know if there is a functionality in R to break histograms
that show a clear bi-modal (or multi-modal) distribution into a series
of unimodal histograms that added up result in the original histogram?
I was thinking of using QQ-plots (for which tools are available in R),
and then observing the number of times the observed quantiles cross
the 1:1 line, but this only gives an indication of  how many "peaks"
the current histogram has. Therefore I was wondering whether other
approaches exist.

Thanks in advance for any suggestions.

p.s. also thanks to those who helped me on my previous question on
Modelling different combinations of explanatory variables. The leaps
package and the regsubsets command worked really well!

On 28-Aug-09 10:34:46, Thomas Groen wrote:
> Dear All,
> 
> Does anybody know if there is a functionality in R to break histograms
> that show a clear bi-modal (or multi-modal) distribution into a series
> of unimodal histograms that added up result in the original histogram?
> I was thinking of using QQ-plots (for which tools are available in R),
> and then observing the number of times the observed quantiles cross
> the 1:1 line, but this only gives an indication of  how many
"peaks"
> the current histogram has. Therefore I was wondering whether other
> approaches exist.
> 
> Thanks in advance for any suggestions.
> 
> p.s. also thanks to those who helped me on my previous question on
> Modelling different combinations of explanatory variables. The leaps
> package and the regsubsets command worked really well!
There are a number of points of information which would help us to
be more specific about suggestions.

1: Do you have the raw data from which the histogram was constructed?
Decomposition of a multimodal sample into constituent unimodal
components is best done by adopting a generic distirbution type
(e.g. Normal) for each component, and then estimating the paramaters
of each component from the data. There is more information (and
there better estimation) in the raw data than in the histogram.

2: Do you have a preferred generic distribution type (e.g. Normal)
for the component distributions?
(If not, and you don't care what distribution you adopt, then
what is to stop you drawing arbitary dividing lines between the
peaks, and asserting that what lies between two consecutive
divisions is one component of the mixture? Then you would end up
with a set of disjoint histograms, one for each component, chosen
in a somewhat arbitrary way. Since you presumably don't intend
that to happen, you presumably have reasons why it should not
happen which would amount to a preference for generic distribution
type).

Once the generic type is chosen, a specific method is indicated.
For example, do an R Site Search on "normal mixture" in
"Functions"
at:

  http://finzi.psych.upenn.edu/nmz.html

You may want to look at

http://finzi.psych.upenn.edu/R/library/mclust/html/00Index.html
("Model-Based Clustering / Normal Mixture Modeling").

Ted.

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Date: 28-Aug-09                                       Time: 12:12:36
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