R: Generating Random Effects in Mixed-Effect Models

mkran {gss} | R Documentation

## Generating Random Effects in Mixed-Effect Models

### Description

Generate entries representing random effects in mixed-effect models.

### Usage

    mkran(formula, data)
    mkran1(ran1, ran2)

### Arguments

`formula` | Symbolic description of the random effects.
`data` | Data frame containing the variables in the model.
`ran1` | Random effects in the form of the value of `mkran`

.

`ran2` | Random effects in the form of the value of `mkran`

.

### Details

`mkran` generates random effect terms from simple grouping variables, for use in nonparametric mixed-effect models as described in Gu and Ma (2005a, b). The syntax of the formula resembles that of similar utilities for linear and nonlinear mixed-effect models, as described in Pinheiro and Bates (2000).

Currently, `mkran` takes only two kinds of basic formulas, `~1|grp2` or `~grp1|grp2`. Both `grp1` and `grp2` should be factors, and for the second formula, the levels of `grp2` should be nested under those of `grp1`.

The Z matrix is determined by `grp2`. When observations are ordered according to the levels of `grp2`, the Z matrix is block diagonal of 1 vectors.

The Sigma matrix is diagonal. For `~1|grp2`, it has one tuning parameter. For `~grp1|grp2`, the number of parameters equals the number of levels of `grp1`, with each parameter shared by the `grp2` levels nested under the same `grp1` level.

`mkran1` adds together two independent random effects, and can be used recursively to add more than two terms. The arguments are of the form of the value of `mkran` or `mkran1`, which may or may not be created by `mkran` or `mkran1`.

Multiple terms of random effects can also be specified via the likes of `mkran(~1|grp1+1|grp2,data)`, which is equivalent to `mkran1(mkran(~1|grp1,data),mkran(~1|grp2,data))`.

### Value

A list of three elements.

`z` | Z matrix.
`sigma` | Sigma matrix to be evaluated through `sigma$fun(para,sigma$env)`.
`init` | Initial parameter values.

### Note

One may pass a formula or a list to the argument `random` in calls to `ssanova` or`gssanova` to fit nonparametric mixed-effect models. A formula will be converted to a list using `mkran`. A list should be of the same form as the value of `mkran`.

### References

Gu, C. and Ma, P. (2005), Optimal smoothing in nonparametric mixed-effect models. The Annals of Statistics, 33, 1357–1379.

Gu, C. and Ma, P. (2005), Generalized nonparametric mixed-effect models: computation and smoothing parameter selection. Journal of Computational and Graphical Statistics, 14, 485–504.

Pinheiro and Bates (2000), Mixed-Effects Models in S and S-PLUS. New York: Springer-Verlag.

### Examples

    ## Toy data
    test <- data.frame(grp=as.factor(rep(1:2,c(2,3))))
    ## First formula
    ran.test <- mkran(~1|grp,test)
    ran.test$z
    ran.test$sigma$fun(2,ran.test$sigma$env) # diag(10^(-2),2)
    ## Second formula
    ran.test <- mkran(~grp|grp,test)
    ran.test$z
    ran.test$sigma$fun(c(1,2),ran.test$sigma$env) # diag(10^(-1),10^(-2))
    ## Clean up
    ## Not run: rm(test,ran.test)

[Package gss version 2.2-2 Index]