What variable type to choose for a Poisson distributed variable if software package only allows for nominal, ordinal or continuous In the area of cluster analysis I want to calculate the dissimilarity for my data (actual use case is to feed in the dissimilarities into a plotting function to calculate so called silhouette plots).
Now, one of my variables follows a Poisson distribution and I'm actually unsure what would be the best/closest variable type for this kind of data, or if necessary what steps I'd need to take to potentially convert from Poisson to sth. else?
Background:
For my purpose I'm using function daisy from R package cluster which requires my columns to be of the following variable types:

Columns of mode numeric (i.e. all columns when x is a matrix) will be
recognized as interval scaled variables, columns of class factor will
be recognized as nominal variables, and columns of class ordered will
be recognized as ordinal variables. Other variable types should be
specified with the type argument. Missing values (NAs) are allowed.

Further:

The list may contain the following components: "ordratio" (ratio
scaled variables to be treated as ordinal variables), "logratio"
(ratio scaled variables that must be logarithmically transformed),
"asymm" (asymmetric binary) and "symm" (symmetric binary variables).
Each component's value is a vector, containing the names or the
numbers of the corresponding columns of x. Variables not mentioned in
the type list are interpreted as usual (see argument x).


Poisson-distributed data are numeric count data. So a strictly nominal coding, which would treat each count value as a separate unordered level of a multi-level categorical variable, would seem to be inappropriate.
Beyond that, it's essentially your choice of what (dis)similarity measure makes the most sense in the context of your study. Do you want the distance from 1 count to 10 counts to be considered the same as the distance from 101 counts to 110 counts? Then you want interval-scaled, numeric coding.
Do you care about the differences in rank-order among the count values but not necessarily the exact count values? Then an ordinal treatment (or ordratio, which I think would be the same here) would be more appropriate.
The "ratio-scaled" nomenclature comes from Stevens's typology and represents numeric data for which ratios can meaningfully be interpreted: "In contrast to interval scales, ratios can be compared using division. Very informally, many ratio scales can be described as specifying 'how much' of something (i.e. an amount or magnitude)," as the above Wikipedia link puts it.
You thus might choose to consider your data to be ratio-scaled, if that makes sense in the context of your study. For example, if you think that the ratio of counts best captures the distances between instances (e.g, the distance from 1 to 10 counts should be equivalent to the distance from 10 to 100 counts), then the logratio choice would make sense.
