Multilevel modelling and time series analysis in ... - ERSO - Swov

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Chapter 2Results and InterpretationThe intercept β 0j now presents the average speed at LengthCentred = 0 (i.e. fora car of average length) and the coefficient in front of LengthCentred indicatesits slope: the change in speed per unit of length (here meters). The deviance (-2*loglikelihood) decreased by 70, i.e. the introduction of car length as apredictor significantly improved the model.2.2.1.4. Two-level random intercept, random slope modelTo investigate whether the relation between speed and the length of a car wasthe same at all measurement locations, the slope of Length will now be allowedto vary randomly across locations too.Model formulation• Click on the Length• Check the box j (IDlocation)• Estimate the parameters by clicking on “Start”Results and Interpretation
2.2 Linear multilevel modelsThe model now has three parts; the first equation specifies the level of theindividual cars and the other two the level of the locations. Both, the intercept β 0jand the coefficient of Length β 1j are now varying across locations with themeans indicated in the second and third equation.The location variance has now become a variance-covariance matrix Ω u : Theupper left number is σ 2 u0, the variance of the intercepts across locations. Itindicates how much the general level of “Speed” varies between groups. Thelower right number is σ 2 u1, the variance of the coefficient for Length acrosslocations. It shows to what extent the relation between “Speed” and“LengthCentered” varies between groups. The lower left number is thecovariance between the two, indicating to what extent there is a relationbetween the intercept (i.e. the general level of “Speed”) and the slope (i.e. thestrength of the relation to “LengthCentred”) across locations. While the twovariances can only be positive, the covariance can be positive or negative. Apositive covariance indicates that larger intercepts are associated with largerslopes. The opposite is true for a negative covariance.The deviance decreased by 181 as opposed to the variance component model,indicating that there is indeed substantial variation across locations in the effectthat length has on speed. This also becomes apparent in the fact that thevariance of the slope is significant. However the covariance between slope andintercept is not, indicating that there is no relation between the average level ofspeed (i.e. the intercept) and the length effect (i.e. the slope).Graphic inspection of the model predictionsTo interpret the results it can often help to make use of MLwiNs great graphicalfunctions. In this case we will plot the predicted speed values for each location.To do so, we have to save the model-predictions as a new variable first.• Select “Model” in the top menu bar and click on “Predictions”• Click on all parameters in the lower half of the appearing dialogue window(so that they turn from grey to black)• Select an empty column (e.g. c10) for “output from prediction to”• Click on “Calc”• Now you can close the “Predictions” windowP r o j e c t c o - f i n a n c e d b y t h e E u r o p e a n C o m m i s s i o n , D i r e c t o r a t e - G e n e r a l T r a n s p o r t a n d E n e r g yP a g e 1 9
Page 1 and 2: Deliverable D7.5Multilevel modellin
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Page 5 and 6: Chapter 1 - IntroductionHeike Marte
Page 7 and 8: IntroductionFigure 1.2: Structure o
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Chapter 2Another issue that needs t
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Chapter 2In the bottom line of the
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2.4 Longitudinal dataHeike Martense
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Chapter 2Than open the “Names”
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Chapter 2• Click “Calc” to ca
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Chapter 2Results and Interpretation
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Chapter 2Results and Interpretation
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Chapter 2Now a variable that contai
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Chapter 2 Click “Done”• Estim
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Chapter 2As described in the multiv
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Chapter 2▪ Click on resp1 or resp
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Chapter 2Before we proceed in fitti
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Chapter 2▪ Click on the Estimates
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Chapter 2We will now proceed in bui
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Chapter 2A significant regional var
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Chapter 2▪ Click More to run the
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Chapter 2The fixed effect of enforc
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Chapter 3 - Time series analysis3.1
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Chapter 3manual's objective: "even
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Chapter 3The option “Variable Vie
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Chapter 3The figure displayed below
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Chapter 3
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Chapter 3Then mark and click the va
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Chapter 3The residual analysis in t
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Chapter 3A new window “Linear Reg
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Chapter 3The result stated above sh
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Chapter 3The same result is obtaine
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Chapter 3In this new opened window
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Chapter 3To compute the last variab
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Chapter 3
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Chapter 3time series on “Squared
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Chapter 33.2.2 Generalized linear m
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Chapter 3SPSS (Version 14.0) was us
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Chapter 33.4.2 ARIMA models for sta
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Chapter 3• Click on Graphs..Seque
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Chapter 3The ACF plot indicates the
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Chapter 3The ACF plot of the filter
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Chapter 3• Click on Statistics th
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Chapter 3Model Description ARIMA(0,
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Chapter 3In addition to the precedi
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Chapter 3Note that it is very diffi
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Chapter 3In the case the Residuals
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Chapter 3The normal Q-Q plot compar
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Chapter 33.4.4 ARIMA models for sea
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Chapter 33.4.4.2. Model identificat
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Chapter 3The ACF plot indicates obv
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Chapter 33.4.4.3. Model estimation
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Chapter 3• Click on Plots tab and
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Chapter 3Model Description ARIMA (2
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Chapter 33.4.4.4. Graphical results
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Chapter 3Kolmogorov-Smirnov TestIn
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Chapter 3Here are the SPSS results
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Chapter 3of the residuals, up to or
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Chapter 3HistogramQQ-plot
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Chapter 3As the intervention variab
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Chapter 3The addition of the two ex
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Chapter 3Histogram
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Chapter 3Kolmogorov-Smirnov TestIn
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Chapter 33.5 DRAG modelsThe DRAG mo
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Chapter 3a summary of results and s
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Chapter 3This data file consists of
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Chapter 3 Then click on the Finish
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Chapter 3Independence Q(6,6) 28.8 1
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Chapter 3Step 4: Graphics of model
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Chapter 3 Shortly examine the figur
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Chapter 3The STAMP graphics window
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Chapter 334, we better use the Door
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Chapter 3The auxiliary residuals ar
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Chapter 33.6.2.2 Stochastic level m
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Chapter 3convergence criteria used
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Chapter 36.25Log_NO_fatTrend_Log_NO
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Chapter 3 Go to the STAMP window ag
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Chapter 3 Click OK.
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Chapter 3The list of forecast resul
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Chapter 33.6.3 Local linear trend m
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Chapter 3Irr 0.021360 ( 1.0000) Che
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Chapter 3 In the Residual graphics
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Chapter 33.6.3.2. Stochastic linear
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Chapter 3Estimation sample is 1970.
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Chapter 37.0 Log_FI_fat Trend_Log_F
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Chapter 3The goodness-of-fit is cle
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Chapter 3The STAMP graphics window
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Chapter 33.6.4 Local linear trend p
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Chapter 3Prediction error variance
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Chapter 3Parameter estimation sampl
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Chapter 38.007.757.507.257.000.2Log
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Chapter 3Goodness-of-fit results fo
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Chapter 3interpretation of the test
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Chapter 3The text "Lvl 1983.2" appe
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Chapter 3Normality N 2.40 5.99 +Tab
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Chapter 32Residual Log_UKdriversKSI
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Chapter 32IrrRes Log_UKdriversKSI0.
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Chapter 33.6.6 Explanatory variable
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Chapter 3function has increased fro
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Chapter 3Figure 3.6.18: Observed lo
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Chapter 3 Use the menu or to save
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Chapter 32IrrRes Log_UKdriversKSI0.
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Chapter 3for this period. The actua
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Chapter 3the top figure and the ori
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Chapter 4 - ConclusionThe present d
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Chapter 4researchers conduct valid
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ReferencesLISREL for Windows. Scien
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