Negative binomial models fitted the data better than ...
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Effect of Decriminalization of Suicide in 1993 in Ireland on suicidal deaths: a comparison between standard and linear Poisson and negative binomial autoregressive models, and ARIMAX model
Introduction Moving average and autoregressive Poisson modelling of time series data was proven to have many advantages over standard event count models [Brandt et al 2000]. Moreover, it is claimed that such models overcome the inefficiency of standard time series analysis when the data are specifically non-Gaussian [Brandt et al 2001]. Certainly, if systematic patterns of systematic dynamics are not accounted for properly, any inferences made will be incorrect. Such problems were tackled, somewhat dissatisfactorily, by applying a standard Gaussian ARIMA anyway, applying a standard negative binomial modelling of the count data, or by transformation prior to application of standard time series analysis [King et al 1988,King et al 1989].
Method We utilized the suicide deaths count data in Ireland between 1970 and 2000. The data were requested from the CSO vital statistics section. We carried out the intervention analysis by including a binary variable for the effect of the Decriminalization of Suicide Act that came into force in 1993, non-zero from that year onward. Identification of the autoregressive model was carried out by investigating the behaviour of the auto-correlation and the partial autocorrelation functions. We applied standard Poisson and negative binomials, autoregressive Poisson and negative binomial models to the suicide deaths count data with an offset term to account for the population count. We also applied and ARIMAX model to the suicide data. Comparison between models was carried out based on fulfilment of the underlying assumptions, log-likelihood calculation, and AIC index.
Results Table 1: Comparing standard and autoregressive models with ARIMAX model for the 1970-2000 Irish suicide data Negative Variable/Model Binomial Year -115 Year SD 7.826 Year p value
