Strategies for construction hazard recognition
Table 2: Interrupted time series regression models
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- Figure 1: Mathematical model selection flowchart for analysis
| Table 2: Interrupted time series regression models Type of Intervention Parameters Assumed Relationship among Errors Level Change and Slope Change Level Change Only Independent Model I Four-parameter Model II Two-parameter Y t = β 0 + β 1 T t + β 2 D t + β 3 SC t + ε t Y t = β 0 + β 2 D t + ε t Autocorrelated Model III Four-parameter Model IV Two-parameter Y t = β 0 + β 1 T t + β 2 D t + β 3 SC t + tut Yt 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 = 0; 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 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 tb Figure 1: Mathematical model selection flowchart for analysis Fit Models I and II using Ordinary least squares Model Comparison Accept H 0 Test for autocorrelated errors Select Model II Reject H 0 Test for autocorrelated errors Accept H 0 Reject H 0 Accept H 0 Reject H 0 Select Model IV Select Model I Select Model III 95 𝐹 = (𝑆𝑆 𝑅𝑒𝑔 𝑀𝑜𝑑𝑒𝑙𝐼 − 𝑆𝑆 𝑅𝑒𝑔 𝑀𝑜𝑑𝑒𝑙𝐼𝐼 )/2 𝑀𝑆 𝑅𝑒𝑔 𝑀𝑜𝑑𝑒𝑙𝐼 (2) Where SS Reg ModelI 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 Before making the final conclusion regarding the appropriate model, the assumption of independent errors (autocorrelation) was tested. Observations are said to be autocorrelated when errors measured at time t would predict errors associated with measurements taken at a later point in time (e.g. t+1). The Durbin-Watson test was used to test the null hypothesis that the lag autocorelation among the observations were equal to zero (ρ=0). In addition to the Durbin- Watson test, the Huitema-McKean test of autocorrelation was computed since the Durbin- Watson test provides inconclusive results when the test statistic falls between the two critical values. If the tests suggested that the errors were autocorrelated, then alternate models which take autocorrelated errors into consideration must be used (Model III or Model IV. After the appropriate model is determined, the coefficients of the regression equation provides the measure of change, either improvement or decline in terms of the level-change and the slope- change coefficient. Based on these aggregate results of all the three crews, then an overall level change and slope change test statistic was computed using the reciprocal of error variance as shown in Equation 3. 𝐿𝐶 𝑜𝑣𝑒𝑟𝑎𝑙𝑙 = ∑ 1 𝜎 𝑗 2 𝑏 𝐿𝐶 𝑗 𝐽 𝑗=1 ∑ 1 𝜎 𝑗 2 𝐽 𝑗=1 (3) 96 Where J is the number of crews is the level change coefficent estimated for the jth crew is the estimated standard error for the jth level change coefficient Download 2.75 Mb. Share with your friends:
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