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

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Chapter 3Prediction error variance is 0.00556772Summary statisticsLog_UKdriverStd.Error 0.074617Normality 3.7108H( 59) 1.0905r( 1) 0.026288r(12) 0.029382DW 1.9311Q(12, 9) 12.378Rs^2 0.23046Eq 4 : Estimated variances of disturbances.Component Log_UKdriversKSI (q-ratio)Irr 0.0034678 ( 1.0000)Lvl 0.0010009 ( 0.2886)Slp 0.00000 ( 0.0000)Sea 0.00000 ( 0.0000)Inspecting the estimated variances of the disturbances, we see that thevariances corresponding to the slope component (Slp) and the seasonalcomponent (Sea) are (almost) equal to zero. Therefore, we repeat the analysis(steps 2 and 3) with a deterministic slope and seasonal component (bychoosing Stochastic level, Fixed slope, and Fixed seasonal in the STAMPSelect components window). This yields the following output in the GiveWinresults window:Equation 5.Log_UKdriversKSI = Trend + Fixed seasonal + IrregularEstimation reportModel with 2 parameters ( 1 restrictions).Parameter estimation sample is 1969. 1 - 1984.12. (T = 192).Log-likelihood kernel is 2.279365.Very strong convergence in 3 iterations.( likelihood cvg 1.23912e-013gradient cvg 3.566036e-008parameter cvg 3.127122e-007 )Eq 5 : Diagnostic summary report.Estimation sample is 1969. 1 - 1984.12. (T = 192, n = 190).Log-Likelihood is 437.638 (-2 LogL = -875.276).Prediction error variance is 0.00550388Summary statisticsLog_UKdriverStd.Error 0.074188Normality 2.9938H( 63) 1.0297r( 1) 0.029490r(12) -0.0070854DW 1.9343Q(12,11) 12.196Rs^2 0.23928Eq 5 : Estimated variances of disturbances.Component Log_UKdriversKSI (q-ratio)Irr 0.0034678 ( 1.0000)Lvl 0.0010009 ( 0.2886)
3.6 State space models Check the results (sample period, log-likelihood, estimated variance ofdisturbances).The estimation report tells that there was very strong convergence in three iterations. Thediagnostic summary report shows that the number of observations is 192, that the value of thelog-likelihood function at convergence is 437, and that the prediction error variance is 0.00550.The estimated variance of the level disturbances is unequal to zero. In the STAMP window choose in the menu. Select Additional output, Get steady state, Anti-log analysis, and State andregression output. Click OK.The GiveWin Results window will display the following additional results:Eq 5 : Estimated standard deviations of disturbances.Component Log_UKdriversKSI (q-ratio)Irr 0.058888 ( 1.0000)Lvl 0.031637 ( 0.5372)Eq 5 : Estimated coefficients of final state vector.Variable Coefficient R.m.s.e. t-valueLvl 7.2404 0.038792 186.65 [ 0.0000]Slp -0.00090532 0.0023076 -0.39233 [ 0.6953]Sea_ 1 0.017176 0.016254 1.0567 [ 0.2920]Sea_ 2 -0.10933 0.016219 -6.7409 [ 0.0000]Sea_ 3 -0.070091 0.016192 -4.3288 [ 0.0000]Sea_ 4 -0.14686 0.016171 -9.0817 [ 0.0000]Sea_ 5 -0.055472 0.016157 -3.4333 [ 0.0007]Sea_ 6 -0.092507 0.016150 -5.7279 [ 0.0000]Sea_ 7 -0.043175 0.016150 -2.6734 [ 0.0082]Sea_ 8 -0.032024 0.016157 -1.982 [ 0.0489]Sea_ 9 0.0058909 0.016171 0.36429 [ 0.7160]Sea_10 0.086848 0.016192 5.3637 [ 0.0000]Sea_11 0.19221 0.016219 11.851 [ 0.0000]Anti-log trend analysisTrend value at end of period is 1394.63.Growth rate at end of period is -0.000905317 ( -1.08638 % per“year”).From the estimated coefficients of the final state vector and their t-values, we can conclude thatthe (constant) value of -0.00090532 for the slope component does not significantly deviate fromzero. The same applies to the values for the first and ninth estimates of the seasonalcomponent (corresponding to the months of January and September).Because the deterministic slope component is not significantly different fromzero, we drop the slope component from the model and repeat the analysis(steps 2 and 3) with a stochastic level deterministic seasonal model (byselecting Stochastic level and Fixed seasonal in the STAMP Select componentswindow). This yields the following output in the GiveWin results window:Equation 6.Log_UKdriversKSI = Level + Fixed seasonal + IrregularEstimation reportModel with 2 parameters ( 1 restrictions).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 3 5
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Deliverable D7.5Multilevel modellin
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3.6 State space models.............
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Chapter 1 - IntroductionHeike Marte
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IntroductionFigure 1.2: Structure o
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2.1 Introduction multilevel modelli
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2.2 Multilevel linear regression mo
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2.2 Linear multilevel models Click
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2.2 Linear multilevel modelsResults
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2.2 Linear multilevel models• Cli
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2.2 Linear multilevel modelsThe mod
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2.2 Linear multilevel modelsThe siz
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Chapter 2intercept between location
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Chapter 2Results and interpretation
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2.3 Discrete response models2.3.1 I
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Chapter 2• Click on “Add Term
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Chapter 2Predictor Coefficient π j
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2.3.3 Multinomial responsesHeike Ma
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Chapter 2A new response variable ha
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Chapter 2ResultsAs can be seen in t
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Chapter 2• Select “age” from
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2.3.4 CountsGeorge Yannis, Eleonora
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Chapter 2▪ Click on the N (ΩΧ,
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Chapter 2These results are intuitiv
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Chapter 2▪ In the plot what? tab,
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Chapter 2We will now add a random s
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Chapter 2All fixed and random effec
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Chapter 2We can see that the level-
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Chapter 2In this case, all fixed ef
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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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Page 248 and 249: Chapter 32Residual Log_UKdriversKSI
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Page 270: ReferencesLISREL for Windows. Scien
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