Investigators noted that the Deviance divided by the d.f. was greater than two. This could be an indication of which of the following? (List all that apply.)

a. There is more variability in the responses than one would expect with the Poison distribution.

b. There are interactions between two or more of the predictors.

c. The sample of infants used for the study was not an independent, random sample.

d. The investigators should dichotomize one of the continuous predictors to yield clearer policy implications.

e. The estimation algorithm to estimate the regression parameters had difficulty converging.
Transcribed Image Text:APPENDIX 1 A study examined families in three major cities in Thailand. The study focused on infant development in the context of the backgrounds and living conditions of families. 269 observations with complete observations are included in this analysis. Investigators studied predictors of infant behavioral characteristics. One of the characteristics "Excitability" was measured as the number of times an infant acted "excited" in a on hour period of time. Potential predictors included the baby's gestational age (gestation_weeks), the quality of the families living conditions (qols), mother's language-free nonverbal intelligence (TONI4_INDEX), the numbers of years of education of the father (FatherYrs Educ), the number of preterm births the mother had experienced (Preterm), and infant sex (0=female, 1=male). Below is relevant SAS Output. 0.0150 The GENMOD Procedure Model Information 0.0748 Data Set Distribution Link Function Dependent Variable WORK.ALL MERGED Poisson Log Excitability Number of Observations Read320 Number of Observations Used269 Missing Values Parameter Information ParameterEffect Prm1 Intercept Prm2 gestation_weeks Prm3 Qols Prm4 TONI4 INDEX Prm5 Father YrsEduc Prm6 Preterm Prm7 Infantsex 51 Criteria For Assessing Goodness Of Fit Criterion Deviance Scaled Deviance DF ValueValue/DF 262 577.3168 2.2035 262 577.3168 2.2035 Pearson Chi-Square Scaled Pearson X2 Log Likelihood Full Log Likelihood AIC (smaller is better) 262 566.3297 2.1616 262 566.3297 2.1616 -248.4164 -463.6072 941.2145 AICC (smaller is better) 941.6436 966.3774 BIC (smaller is better) Algorithm converged. Analysis Of Maximum Likelihood Parameter Estimates Standard Wald 95% Confidence Wald Chi- Parameter DFEstimate Error Limits Square Pr> ChiSq Intercept 1 0.2324 1.8543 -3.4020 3.8667 0.02 0.9003 gestation_weeks 1 -0.0190 0.0474 -0.1120 0.0739 0.16 0.6881 qols 1 -0.1267 0.0958 -0.3145 0.0610 1.75 0.1858 TONI4 INDEX 1 0.0034 0.0072 -0.0106 0.0174 0.22 0.6366 Father YrsEduc 1 0.0454 0.0150 0.0160 0.0748 9.14 0.0025 Preterm 1 -0.8756 0.3012 -1.4660 -0.2853 8.45 0.0036 infantsex 1 0.0712 0.1102 -0.1448 0.2871 0.42 0.5184 Scale 0 1.0000 0.0000 1.0000 1.0000 Note: The scale parameter was held fixed.

Question

Investigators noted that the Deviance divided by the d.f. was greater than two. This could be an indication of which of the following? (List all that apply.)

a. There is more variability in the responses than one would expect with the Poison distribution.

b. There are interactions between two or more of the predictors.

c. The sample of infants used for the study was not an independent, random sample.

d. The investigators should dichotomize one of the continuous predictors to yield clearer policy implications.

e. The estimation algorithm to estimate the regression parameters had difficulty converging.

APPENDIX 1
A study examined families in three major cities in Thailand. The study focused on infant
development in the context of the backgrounds and living conditions of families.
269 observations with complete observations are included in this analysis. Investigators studied
predictors of infant behavioral characteristics. One of the characteristics "Excitability" was
measured as the number of times an infant acted "excited" in a on hour period of time. Potential
predictors included the baby's gestational age (gestation_weeks), the quality of the families living
conditions (qols), mother's language-free nonverbal intelligence (TONI4_INDEX), the numbers of
years of education of the father (FatherYrs Educ), the number of preterm births the mother had
experienced (Preterm), and infant sex (0=female, 1=male). Below is relevant SAS Output.
0.0150
The GENMOD Procedure
Model Information
0.0748
Data Set
Distribution
Link Function
Dependent Variable
WORK.ALL MERGED
Poisson
Log
Excitability
Number of Observations Read320
Number of Observations Used269
Missing Values
Parameter Information
ParameterEffect
Prm1
Intercept
Prm2
gestation_weeks
Prm3
Qols
Prm4
TONI4 INDEX
Prm5
Father YrsEduc
Prm6
Preterm
Prm7
Infantsex
51
Criteria For Assessing Goodness Of Fit
Criterion
Deviance
Scaled Deviance
DF ValueValue/DF
262 577.3168 2.2035
262 577.3168 2.2035
Pearson Chi-Square
Scaled Pearson X2
Log Likelihood
Full Log Likelihood
AIC (smaller is better)
262 566.3297 2.1616
262 566.3297 2.1616
-248.4164
-463.6072
941.2145
AICC (smaller is better)
941.6436
966.3774
BIC (smaller is better)
Algorithm converged.
Analysis Of Maximum Likelihood Parameter Estimates
Standard Wald 95% Confidence
Wald Chi-
Parameter
DFEstimate
Error
Limits
Square Pr> ChiSq
Intercept
1
0.2324 1.8543
-3.4020
3.8667
0.02 0.9003
gestation_weeks 1 -0.0190 0.0474
-0.1120
0.0739
0.16
0.6881
qols
1 -0.1267 0.0958
-0.3145
0.0610
1.75
0.1858
TONI4 INDEX 1 0.0034 0.0072
-0.0106
0.0174
0.22
0.6366
Father YrsEduc
1 0.0454 0.0150
0.0160
0.0748
9.14
0.0025
Preterm
1 -0.8756 0.3012
-1.4660
-0.2853
8.45
0.0036
infantsex
1 0.0712 0.1102
-0.1448
0.2871
0.42
0.5184
Scale
0 1.0000 0.0000
1.0000
1.0000
Note: The scale parameter was held fixed.

Accepted Answer

a. There is more variability in the responses than one would expect with the Poisson distribution.…