# plot.simplexreg: Plots for simplexreg Objects In simplexreg: Regression Analysis of Proportional Data Using Simplex Distribution

## Description

Various types of plots could be produced for simplexreg Objects, including plots of correlation structure, plots of different types of residuals and plots of partial deviance.

## Usage

 ```1 2``` ```## S3 method for class 'simplexreg' plot(x, type = c("residuals", "corr", "GOF"), res = "adjvar", lag = 1, ...) ```

## Arguments

 `x` fitted model object of class "simplexreg" `type` character specifying types of plots: the correlation (`corr`), residuals (`residuals`), partial deviances (`GOF`). See 'Details' `res` character specifying types of residuals:approximate Pearson residual (`appstdPerr`), standard Pearson residual (`stdPerr`), adjusted dependent variable s_i (`adjvar`). See `residuals.simplexreg` `lag` when `type = corr`, this function examine the autocorrelation at lag `lag` `...` other parameters to be passed through to the plot function

## Details

This function provides graphical presentations for simplexreg objects. The plot of correlation aims examine the correlation structure of the longitudinal data set. Let r_{ij} be the standardised score residuals of the `i`th observation at time t_{ij}, and `lag = k`, then r_{ij} are plotted against r_{ik} for all i and j < k, if |t_{ij} - t_{ik}| = k.

Residuals can be plotted when specifying `type = "residuals"`, The upper and lower 95 (1.96) are also lined.

Plots of partial deviance are for the goodness-of-fit test in the presence of within-subject dependence for longitudinal data. The partial deviances are defined as

D_j^P=sum d(y_{ij}-mu_{ij}) / σ_{ij}^2, j in T

where T denotes a collection of all distinct times on which observation are made. Cross-sectionally, y_{ij}'s are independent and hence D_j^P follows approximately χ^2, with m_j being the total number of y_{ij}'s observed cross-sectionally at time t_j. Both observed partial deviance D_j^P statistics and the corresponding critical values are depicted and compared at each time point.

Chengchun Shi

## References

Song, P. and Qiu, Z. and Tan, M. (2004) Modelling Heterogeneous Dispersion in Marginal Models for Longitudinal Proportional Data. Biometrical Journal, 46: 540–553

Qiu Z. (2001) Simplex Mixed Models for Longitudinal Proportional Data. Ph.D. Dissertation, York University

Zhang, P. and Qiu, Z. and Shi, C. (2016) simplexreg: An R Package for Regression Analysis of Proportional Data Using the Simplex Distribution. Journal of Statistical Software, 71: 1–21

`summary.simplexreg`, `residuals.simplexreg`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13``` ```## fit the model data("sdac", package="simplexreg") sim.glm2 <- simplexreg(rcd~ageadj+chemo|age, link = "logit", data = sdac) data("retinal", package = "simplexreg") sim.gee2 <- simplexreg(Gas~LogT+LogT2+Level|LogT+Level|Time, link = "logit", corr = "AR1", id = ID, data = retinal) ## produce the plots plot(sim.glm2, type = "residuals", res = "stdPerr", ylim = c(-3, 3)) plot(sim.gee2, type = "corr", xlab = "", ylab = "") plot(sim.gee2, type = "GOF", xlab = "", ylab = "") ```