Strategies for construction hazard recognition
Table 2: Interrupted time series regression
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- Model II Two-parameter (Level change only) Yt= β0+ β2Dt+ εtAutocorrelated
| Table 2: Interrupted time series regression Intervention parameters Relationship among Errors Independent Model I Four-parameter (Level change and slope change) Y t = β 0 + β 1 T t + β 2 D t + β 3 SC t + ε t Model II Two-parameter (Level change only) Y t = β 0 + β 2 D t + ε t Autocorrelated Model III Four-parameter (Level change and slope change) Y t = β 0 + β 1 T t + β 2 D t + β 3 SC t + tut bModel IV Two-parameter (Level change only) Y t = β 0 + β 2 D t + tut Where, Y t is the dependent variable (hazard identification level) at time t β 0 is the intercept of the regression line at t = is the slope at the baseline phase; β 2 is the level change measured at time n is the change in slope from the baseline phase to the intervention phase T t is the value of the time variable Tat time t D t is the value of the level-change dummy variable D (0 for the baseline phase and 1 for the intervention phase) at time t SC t is the value of the slope-change variable SC defined as [T t -( n+ D n 1 is the number of observations in the baseline phase; ε t is the error of the process at time t φ 1 is the lag autoregressive coefficient u t is Y t - (β 0 + β 1 T t + β 2 D t + β 3 SC t + tat time t. Figure 4 illustrates the mathematical model selection procedure. The first step in the determination of the appropriate model involved estimating Model I and II. Both models were estimated by regressing the dependant variable (HR index) on their respective predictor variables. After the parameters were estimated, the two models were compared by testing the null hypothesis that a trend/slope does not exist in either phase ( β 1 = β 3 = 0) using the test statistic 59 shown in Equation 2. A slope change may have been induced as a result of the intervention, or the baseline data may exhibit a slope. If the null hypothesis is accepted, then β 1 and β 3 can be assumed to be zero, and the resulting equation will reduce to the form in Model II representing only level change. In this case, Model II is more suitable for representing the observed data, and the statistical power of the testis higher due to the fewer number of parameters involved. On the other hand, if the alternate hypothesis is accepted, then Model II would bias the level change estimate because the slope change is not adequately represented. The second step involves the testing of the assumption of independent errors, also known as autocorrelation. When repeated measures are gathered on a continual basis, there is a possibility that the errors measured at a given time t could provide sufficient information to predict errors at subsequent periods (e.g. t+1). The presence of autocorrelation with the observed data can lead to erroneous statistical inferences if the selected model does not account for autocorrelation. Thus, we used the Durbin-Watson test to test the null hypothesis that the lag autocorrelation among errors is equal to zero ( ρ=0). Because the Durbin-Watson test provided inconclusive results when the test statistic falls between the two critical values, we also computed the Huitema-McKean test statistic for autocorrelation. If the test reveals that the errors are autocorrelated, then Model III should be used when a slope is present in either phase, or Model IV should be used if slope is absent in both phases. 𝐹 = (𝑆𝑆 𝑅𝑒𝑔 𝑀𝑜𝑑𝑒𝑙𝐼 − 𝑆𝑆 𝑅𝑒𝑔 𝑀𝑜𝑑𝑒𝑙𝐼𝐼 )/2 𝑀𝑆 𝑅𝑒𝑔 𝑀𝑜𝑑𝑒𝑙𝐼 (2) 60 Where 𝑆𝑆 𝑅𝑒𝑔 is the regression sum of squares based on model I 𝑆𝑆 𝑅𝑒𝑔 is the regression sum of squares based on model II and 𝑀𝑆 𝑅𝑒𝑔 is the residual mean squares based on model I Download 2.75 Mb. Share with your friends:
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