Leff: Hypothesis matrices for first and higher-order effects

In gmonette/spida15: Collection of miscellaneous functions for mixed models etc. prepared for SPIDA 2009+ (development version)

Description

Easier visualization, estimation, testing and graphing of specific effects in models with complex interactions.

Usage

Leff(fit, x = NULL, data, debug = F)

Arguments

fit	a model with a linear formula.
x	the name of the variable(s) with respect to which specific effects are needed
data	a data frame of values where specific effects are estimated
debug

Details

Functions for effect plots Leff, Leff2 - generate L matrices for effect plots and second order effect plots Linfo - information on variables in model Lallterms - show all terms that involve an effect Lcall - generate code for manual editing for a cbind call to generate an L matrix Also in this script: onames - pretty labels for variable in xyplot allp - recursive function to generate all permutations

USER'S GUIDE:

Plotting effects: (call the variable of interest 'x')

Effects can be plotted in a number of ways. To help a reader visualize an effect it is probably best to plot them in more than one way:

1) response plot: yhat is plotted against 'x' controlling for other variables

a) variables that have no interactions with 'x' can be set at a value, their only effect on the plot is to move the entire graph up or down but they do not affect the shape of the graph.

b) Variables that do interact significantly with x should be set at different levels and can be visualized with panels ( y ~ x | z) in xyplot or with 'groups'. Different choices will bring different features into prominence.

2) effect plot: the effect of 'x' on 'y' is plotted against other variables that have interactions with 'x'. If 'x' is involved in 3-way or higher interactions, then the effect of 'x can be plotted against one of the interacting variables controlling for others using panels or groups in xyplot.

Response plots are produced in the familiar way: create a 'pred' data frame and then use 'predict' to add yhat to the data frame.

The following discusses the creation of effect plots using a number of tools:

Leff generates an L matrix to estimate the effect of 'x' as a function of other variables

Linfo extracts useful information about variables in a model and their interactions with 'x'

Lallterms generates a list of terms that can be used with 'wald' [essentially it replaces wald(fit , allp3( 'x','y','z')) etc.] Lallterms can be used in a way to generate only the overall F tests without showing the individual terms although it is desirable to look at the individual terms.]

Lcall generates a call to cbind with the code to generate each column of the model matrix. The code can be edited to, e.g., differentiate each term to produce and effect L matrix manually if the effect of a complex term is needed.

The following describes the use of Leff to generate effect plots

Leff generates an L matrix to estimate the effect of a variable as a function of the variables that it interacts with

Limitation: Leff works only for a numerical variable or a factor that enters linearly, e.g. no squares or polynomials or functions To work with a variable that enters in a polynomial, use 'Lcall' and then differentiate each term manually.

Using Leff

1) Choose a linear variable (let's call it x) whose effect you want to explore

2) Study how the effect of x depends on other variables, i.e. what variables have interactions with x in the model. Doing this is simplified by using:

> lallt <- Lallterms ( fit, 'x' ) # generates all terms including x > lallt > wald( fit, Lallterms( fit, 'x' ))

To see just the summary F tests, use:

> summ ( wald( fit, Lallterms( fit, 'x' )) ) or > round ( summ ( wald( fit, Lallterms( fit, 'x' )) ) , 5)

This shows whether the effect of 'x' depends on other variables individually or jointly and provides guidance regarding the effects that should be displayed. For example, if another variable 'z' only has weak interactions, then it may be sufficient to control for 'z' without displaying what happens when 'z' is varied but to simply hold z at a median value.

If a variable has no interactions with 'x', then the effect of 'x' is invariant wrt that variable and the value at which the variable is set is immaterial although one must choose a a value for the function 'Leff' to work.

3) Identify a) the basic variables in the model, and b) the basic variables on which the effect depends, i.e. the basic variables that are involved in interaction with x Doing this is simplified with:

> Linfo( fit, 'x' )

4) Generate response plots: a) generate a prediction data frame with all variables b) plot desired responses curves to show effects

5) Create an effect data frame for effects 'pred.eff' in which all variables in the model appear. a) the basic numerical variables in the model that do not interact with 'x' only need to be present at an arbitrary level (as mentioned above). b) Factors should be present at all levels. e.g. sex = levels(zdc$sex) c) Variables that interact with x should be present in the values you intend to plot d) If x is numerical: include only x = 1 If x is a factor, include it at all its levels: e.g. sex = levels(zdc$sex) The code for the prediction data frame would look like:

pred.eff <- expand.grid( sex = levels(zdc$sex) , age = 12:80, incomez = seq(-4,4,2), x = 1)

6) Generate the effect matrix:

> Lf <- Leff( fit, 'x', pred.eff) # Note 'x' should be in quotes. and inspect it: > head( Lf ) Make sure it makes sense ( this is an experimental function )

7) Estimated the effects using 'wald'

> ww <- as.data.frame( wald( fit, Lf))

Merge with pred.eff

> wc <- cbind( ww, pred.eff)

8) Plot the effect with xyplot.

If 'x' is a factor, you need to select levels of the factor. The effect plot will show the difference between the selected level and the reference level To compare two levels that are NOT reference levels is IN DEVELOPMENT

9) To easily compare the effect at different levels of an interacting variable is laborious and can be done manually (see example below). A more effective way is IN DEVELOPMENT.

9) DONE! Use 'Leff2' See 'tutorial' for example using ch.abused and sex The idea is to set both variable at the value 1

gmonette/spida15 documentation built on May 17, 2019, 7:26 a.m.