Discretised version of counts of faecal coliform bacteria in sea water samples collected at seven locations near Sydney NSW, Australia. There were four “controls”: Longreef, Bondi East, Port Hacking “50”, and Port Hacking “100” and three “outfalls”: Bondi Offshore, Malabar Offshore and North Head Offshore. At each location measurements were made at four depths: 0, 20, 40, and 60 meters. A large fraction of the counts are missing values.
SydColDiscA data frame with 5432 observations on the following 6 variables.
yA factor consisting of a discretisation of counts of faecal coliform count bacteria in sea water samples. The original measures were obtained by a repeated dilution process.
locna factor with levels Longreef,
Bondi East, Port Hacking 50, Port Hacking
100, Bondi Offshore, Malabar Offshore and
North Head Offshore.
deptha factor with levels 0 (0 metres),
20 (20 metres), 40 (40 metres), 60 (60 metres).
ma.comA factor with levels no and yes,
indicating whether the Malabar sewage outfall had been commissioned.
nh.comA factor with levels no and yes,
indicating whether the North Head sewage outfall had been commissioned.
bo.comA factor with levels no and yes,
indicating whether the Bondi Offshore sewage outfall had been commissioned.
The hidden Markov models applied in the paper Turner et al. (1998) and in the paper Turner (2008) used a numeric version of the response in this data set. The numeric response was essentially a square root transformation of the original data, and the resulting values were modelled in terms of a Poisson distribution. See the references for details.
The observations corresponding to each location-depth combination constitute a (discrete valued) time series. The sampling interval is ostensibly 1 week; distinct time series are ostensibly synchronous. The measurements were made over a 194 week period. Due to exigencies of weather, the unreliabitity of boats and other factors the collection times were actually highly irregular and have been rounded to the neares week. Often no sample was obtained at a given site within a week of the putative collection time, in which the observed count is given as a missing value. In fact over 75% of the counts are missing. See Turner et al. (1998) for more detail.
T. Rolf Turner, Murray A. Cameron, and Peter J. Thomson. Hidden Markov chains in generalized linear models. Canadian J. Statist. 26 (1998) 107 -- 125.
Rolf Turner. Direct maximization of the likelihood of a hidden Markov model. Comp. Statist. Data Anal. 52 (2008) 4147--4160.