Sample: PanelDataAnalysisPDAMixed_Model_RejtingBeta.pdf
Sample: PanelDataAnalysisPDAMixed_Model_RejtingBeta.pdf
Uputa: Panel Data Analysis  SPSS Setting Up Mixed Model with No Predictors using Singer Data.pdf
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za Rejting i Beta
No Predictors in the Model iz fajla:xxxxxxxxxxxPDAMoodys_Beta2kG1107No_Predictors.xlsx
.....
Centered Beta as a Fixed and Random Effect in the Model
iz fajla JelenaPDAMoodys_Beta2kG1107FixedRandom.xlsx
Model Dimension^{a} 


Number of Levels 
Covariance Structure 
Number of Parameters 
Subject Variables 

Fixed Effects 
Intercept 
1 

1 

Beta 
1 

1 


Random Effects 
Intercept + Beta^{b} 
2 
Variance Components 
2 
Company 
Residual 


1 


Total 
4 

5 


a. Dependent Variable: Moodys  Credit Ratings. 

b. As of version 11.5, the syntax rules for the RANDOM subcommand have changed. Your command syntax may yield results that differ from those produced by prior versions. If you are using version 11 syntax, please consult the current syntax reference guide for more information. 
Information Criteria^{a} 

2 Restricted Log Likelihood 
51551,701 
Akaike's Information Criterion (AIC) 
51557,701 
Hurvich and Tsai's Criterion (AICC) 
51557,702 
Bozdogan's Criterion (CAIC) 
51583,400 
Schwarz's Bayesian Criterion (BIC) 
51580,400 
The information criteria are displayed in smallerisbetter forms. 

a. Dependent Variable: Moodys  Credit Ratings. 
Estimates of Fixed Effects^{a} 

Parameter 
Estimate 
Std. Error 
df 
t 
Sig. 
95% Confidence Interval 

Lower Bound 
Upper Bound 

Intercept 
,690738 
,126857 
84,003 
5,445 
,000 
,438470 
,943006 
Beta 
,002767 
,001623 
220,783 
1,705 
,090 
,000432 
,005965 
a. Dependent Variable: Moodys  Credit Ratings. 
Znači imamo statističku značajnost (Sig)
The intercept estimate of 0,690738 is the mean of the Moodys  Credit Ratings at the Company level. The Centered Beta estimate of 0,002767 is the slope (rate of change) of the line. It states that for every one point increase in Centered Beta an increase of 0,002767 in Moodys  Credit Ratings will be attained for that student. This is statistically identical to the Centered Beta estimate in the model with Centered Beta as only a fixed effect.
A formula for all this states simply:
S = 0,690738 + 0,002767 y
Where S = Moodys  Credit Ratings Score
y = Company's Centered Beta Score
Estimates of Covariance Parameters^{a} 

Parameter 
Estimate 
Std. Error 




Residual 
2,099164 
,024937 


Intercept [subject = Company] 
Variance 
1,355303 
,211064 


Beta [subject = Company] 
Variance 
,000058 
,000017 


a. Dependent Variable: Moodys  Credit Ratings. 
The residual estimate of 2,099164 is the variability within Companys. The intercept estimate of 1,355303 is the variability of the intercept between Companys and the Beta estimate of 0,000058 is the variability of the Beta between Companys. Thus, the total variability between Companys is 1,355361 (1,355303 + 0,000058).
The residual estimate of 2,099164 is the information that cannot be explained within Companys. It also can be added or subtracted to the equation above to indicate the variability in that equation. The intercept estimate of 1,355303 indicates the variability in the intercept estimate and can be added or subtracted to the intercept estimate above to show the variability. The Beta estimate of 0,000058 indicates the variability in the Beta estimate and can be added or subtracted to the Beta estimate (slope) above to show the variability. (When Centered Beta is a random effect and because it is continuous variable, it gives variability to the slope of the equation, not the intercept.)
Thus:
S = (0,690738 61,355303 ) + (0,002767 60,000058 ) y 6 2,099164
Where S = Moodys  Credit Ratings Score
y = Company's Centered Beta Score
Calculating the Intra Class Correlation (ICC):
ICC _{Centered Beta, Fixed&Random} = 1,355303 / (1,355303 + 2,099164) x 100 = 39,23%
There is important clustering in the model. The ICC indicates that 39,23% of the total variability comes from the variability between the Company and the variability of the Beta between the Company with Centered Beta in the model as a random effect  or that 39,23% of the variability can be explained by the Companys attended and the Beta of the Company. This explains less of the clustering as compared to when Centered Beta was treated as a fixed factor: 38,96%