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The extension of univariate time-series models to multivariate models allows researchers to analyze interdependent time-series data properly.
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Therefore, the multivariate models allowed reliable interpretations.
In this study we have examined both "simple" regression models looking at similar types of factors (e.g. demographic and patient characteristics) as well as more "complex" multivariate models allowing us to test if significance of variables from the like factor model is maintained when "competing" against a wide spectrum of influences.
An F-test to compare the variances in the two groups does not reject the hypothesis that they are identical therefore the multivariate model allows us to test jointly the two lines.
Moreover, the multivariate model allows us to determine the amount of variance in tobacco use accounted for by the other factors assessed in this study.
The multivariate model allowed exclusion of non-significant factors and other possible sources of bias.
The variable treatment protocol and the variables significant at the P < 0.20 level in the univariate analysis were introduced in a multivariate model, allowing for interaction between variables.
Furthermore the absence of a co-morbidity record was included in the multivariate model allowing the model to account for missing variables, particularly as they are not missing at random.
Our multivariate CAR model allows each outcome to have a different neighborhood structure which can utilize different lattices for each structure.
It is possible that other complex multivariate models may allow even greater improvement in performance; however, simultaneous monitoring of data streams may be more practical because univariate models may be applied in a spreadsheet (7 ).
In the multistream analyses, we compared alerts produced by univariate models, which effectively assumed independence between the data streams, and multivariate models, which allowed for correlation between the data streams (Technical Appendix).
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