Polio


  This data set gives the monthly number of cases of poliomyelitis in
  the U.S. for the years 1970--1983 as reported by the Center for
  Disease Control. The polio data frame has 168 rows and 8 columns.


datasets

Functions are provided for estimation, testing, diagnostic checking and forecasting of generalized linear autoregressive moving average (GLARMA) models for discrete valued time series with regression variables.  These are a class of observation driven non-linear non-Gaussian state space models. The state vector consists of a linear regression component plus an observation driven component consisting of an autoregressive-moving average (ARMA) filter of past predictive residuals. Currently three distributions (Poisson, negative binomial and binomial) can be used for the response series. Three options (Pearson, score-type and unscaled) for the residuals in the observation driven component are available. Estimation is via maximum likelihood (conditional on initializing values for the ARMA process) optimized using Fisher scoring or Newton Raphson iterative methods. Likelihood ratio and Wald tests for the observation driven component allow testing for serial dependence in generalized linear model settings. Graphical diagnostics including model fits, autocorrelation functions and probability integral transform residuals are included in the package. Several standard data sets are included in the package.

William TM Dunsmuir

glarma

Generalized Linear Autoregressive Moving Average Models

Polio function

A data frame containing the following columns:
  <table><tr><td>
  [, 1]</td>
<td> Cases </td>
</tr><tr><td> monthly number of cases of poliomyelitis.</td>
<td>
  [, 2]</td>
</tr><tr><td> Intcpt </td>
<td> a vector of ones, providing the intercept in
   the model.</td>
</tr><tr><td>
  [, 3]</td>
<td> Trend </td>
</tr><tr><td> a linear trend.</td>
<td>
  [, 4]</td>
</tr><tr><td> CosAnnual </td>
<td> cosine harmonics at periods of 12.</td>
</tr><tr><td>
  [, 5]</td>
<td> SinAnnual </td>
</tr><tr><td> sine harmonics at periods of 12.</td>
<td>
  [, 6]</td>
</tr><tr><td> CosSemiAnnual </td>
<td> cosine harmonics at periods of 6.</td>
</tr><tr><td>
  [, 7]</td>
<td> SinSemiAnnual </td>
</tr><tr><td> sine harmonics at periods of 6.</td>
<td>
  [, 1]</td>
</tr></table>

Format

Zeger, S.L (1988) A regression model for time series of
  counts. <em>Biometrika</em>, <b>75</b>, 621--629.

Polio: Cases of Poliomyelitis in the U.S.

Description

Usage

Arguments

Format

Source

[, 1]	Cases
monthly number of cases of poliomyelitis.	[, 2]
Intcpt	a vector of ones, providing the intercept in the model.
[, 3]	Trend
a linear trend.	[, 4]
CosAnnual	cosine harmonics at periods of 12.
[, 5]	SinAnnual
sine harmonics at periods of 12.	[, 6]
CosSemiAnnual	cosine harmonics at periods of 6.
[, 7]	SinSemiAnnual
sine harmonics at periods of 6.	[, 1]