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

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Chapter 2o Select 100” indicates that at road sites withmore than 100 cars passing, cars went on average 33.2 km/h faster than onroad sites with fewer than 100 cars passing. The coefficient is highly significant.Moreover the deviance is reduced by 385 as opposed to the model in 2.2.1.4.Both indicates that the number of cars passing at a road sites is a goodpredictor of speed at that road site.2.2.1.7. Testing for a cross-level interactionIn order to test whether the context variable trafficCount modifies the lengtheffectat the level of the individual cars, the interaction between TrafficCountCatand LengthCentred is added to the model.Model formulation• Click on “Add term” and• Include the interaction between LimitCat and LengthCentred as shownbelow Select order 1 (this means it is a first-order interaction) Choose again
2.2 Linear multilevel modelsResults and InterpretationThe coefficient for the interaction (lengthCentred.>100) is clearly not significant,as it is much smaller than its standard error in parenthesis. The negligibleweight for this interaction indicates that the length effect at road sites with morethan 100 cars passing were not different from those at road sites with fewercars passing. The same message is conveyed by the likelihood that did notdecrease from the model in 2.2.1.6 to the present model, suggesting thatadding the interaction introduces complexity that does not explain anything.To conclude, the speed of cars varies more between road sites than withinthem. Accordingly, speed is affected by a level-1 variable (length) to someextent, but much more so by a level-2 variable. The effect of length is notmodified by the traffic count.2.2.1.8. ConclusionIn this chapter it was demonstrated how to extend a linear regression model toa multilevel structure. It was demonstrated how the variance partition coefficientand the deviance test can be used to establish the appropriateness of themultilevel structure and how predictions and residuals at these different levelscan be presented graphically. Moreover, it was explained how effects of level-1predictors (here the length of a car) can be considered together with predictorsat higher levels (here the traffic count at the measurement location) and how aninteraction between variables at different levels can be investigated.P 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 2 5
Page 1 and 2: Deliverable D7.5Multilevel modellin
Page 3 and 4: 3.6 State space models.............
Page 5 and 6: Chapter 1 - IntroductionHeike Marte
Page 7 and 8: IntroductionFigure 1.2: Structure o
Page 9 and 10: 2.1 Introduction multilevel modelli
Page 11 and 12: 2.2 Multilevel linear regression mo
Page 13 and 14: 2.2 Linear multilevel models Click
Page 15 and 16: 2.2 Linear multilevel modelsResults
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Page 28 and 29: Chapter 2intercept between location
Page 30 and 31: Chapter 2Results and interpretation
Page 32 and 33: 2.3 Discrete response models2.3.1 I
Page 34 and 35: Chapter 2• Click on “Add Term
Page 38 and 39: Chapter 2Predictor Coefficient π j
Page 40 and 41: 2.3.3 Multinomial responsesHeike Ma
Page 42 and 43: Chapter 2A new response variable ha
Page 46 and 47: Chapter 2ResultsAs can be seen in t
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Page 56 and 57: Chapter 2These results are intuitiv
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Page 72 and 73: 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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