# Plots for simplexreg Objects

### 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 |

### Arguments

`x` |
fitted model object of class "simplexreg" |

`type` |
character specifying types of plots: the correlation ( |

`res` |
character specifying types of residuals:approximate Pearson residual ( |

`lag` |
when |

`...` |
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.

### Author(s)

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

### See Also

`summary.simplexreg`

, `residuals.simplexreg`

### Examples

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 = "")
``` |