pseudoreplication

[Stefano Larsen]

Hello All,

I was wondering about the sensitivity of NPMR to data with an internal
correlation structure (e.g. multiple sites along the same river, or
longitudinal data in general). Mixed effects models and GEE models
(generalised estimating equations) are traditionally used in these
cases.

How is the story in HyperNiche?

Many thanks

Stefano

[Bruce McCune]

Stefano, This kind of data structure can be handled descriptively in
NPMR in HyperNiche by including variables that code for the groups,
for example, including a single categorical variable for "river" (in
your example) or a series of indicator (0/1) variables for individual
rivers. But HyperNiche currently only offers unconstrained
randomization tests, which will bias the resulting p value from the
test. So HyperNiche could really use some different kinds of
constrained randomizations (corresponding to different data
structures) or randomizations of residuals. For those who would like
a nice, easily digested summary of this, I'd suggest reading Manly's
(1997) "Alternative randomization methods with multiple regression"
in his book, "Randomization, bootstrap and monte carlo methods in
biology". (That's in the 2nd ed., not sure about other editions)

-Bruce McCune

[Ian Pfingsten]

All,

This is similar to my situation with plant population vital rate matrices. I want to maintain the internal correlation structure of the matrices while creating npmr models for each vital rate (element of the matrix) for a number of bootstrapped iterations.

The standard linear approach is to create a correlation matrix of the linear model residuals and cross multiply the square root of that correlation matrix by a set of random normal values and then scale those by the residual standard error of the models. This is like a reverse PCA method in that you find the correlations of the elements in a matrix instead of the orthogonal dimensions. You can then just add these correlated random residuals to the predicted values.

My problem is how to adjust the npmr predictions that don't have residual standard errors. I used a monte carlo method by creating a bootstrapped distribution for each modeled matrix element in order to find a standard deviation. The distributions looked normal, so I used the random normal values cross-multiplied by the same square rooted correlation matrix. However I don't think that I should use a parametric distribution or variation measure with npmr. Any suggestions?

Thanks!
Ian