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Task 2. The following are data on smoking from a survey of seventh graders (age: 1 = 12 or younger, 2 =13 or older): Smoking Family structure Race Gender Age None Some Black Male 1 2 12 Female 1 2 Both parents White Male 1 394 2 Female 1 21 2237 122 2 4 1 32 19 38 2 94 11 Black Male 1 18 1 2 13 1 Female 1 24 0 2 4 3 Mother only White Male 1 48 6 2 25 4 Female 1 55 15 2 13 4 Search for the loglinear model that can best explain the association patterns in the contingency table by treating (a) smoking and family structure as response variables; (b) smoking as a response variable; and the rest as explanatory variables. For consensus, do not drop any terms with p-value close to but less than 0.05 in model search. In each case, i. State the minimal model. ii. Write down the symbol of the loglinear model that best describes the data and give a step-by-step description of how it was built. iii. Represent the conditional independence structure in the loglinear model using an association graph and explain whether it is a graphical model. Give the symbol of another model that has the same association graph, but is not a graphical model. iv. Explain whether the collapsibility condition can be applied and any conditional inde- pendence structure among variables. Interpret the association between smoking and family structure in the loglinear model. v. Explain whether the zero cell in the contingency table affects your analysis.

Task 2. The following are data on smoking from a survey of seventh graders (age: 1 = 12 or younger, 2 =13 or older): Smoking Family structure Race Gender Age None Some Black Male 1 2 12 Female 1 2 Both parents White Male 1 394 2 Female 1 21 2237 122 2 4 1 32 19 38 2 94 11 Black Male 1 18 1 2 13 1 Female 1 24 0 2 4 3 Mother only White Male 1 48 6 2 25 4 Female 1 55 15 2 13 4 Search for the loglinear model that can best explain the association patterns in the contingency table by treating (a) smoking and family structure as response variables; (b) smoking as a response variable; and the rest as explanatory variables. For consensus, do not drop any terms with p-value close to but less than 0.05 in model search. In each case, i. State the minimal model. ii. Write down the symbol of the loglinear model that best describes the data and give a step-by-step description of how it was built. iii. Represent the conditional independence structure in the loglinear model using an association graph and explain whether it is a graphical model. Give the symbol of another model that has the same association graph, but is not a graphical model. iv. Explain whether the collapsibility condition can be applied and any conditional inde- pendence structure among variables. Interpret the association between smoking and family structure in the loglinear model. v. Explain whether the zero cell in the contingency table affects your analysis.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 42PFA
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Task 2. The following are data on smoking from a survey of seventh graders (age: 1 = 12 or younger, 2 =13 or older): Smoking Family structure Race Gender Age None Some Black Male 1 2 12 Female 1 2 Both parents White Male 1 394 2 Female 1 21 2237 122 2 4 1 32 19 38 2 94 11 Black Male 1 18 1 2 13 1 Female 1 24 0 2 4 3 Mother only White Male 1 48 6 2 25 4 Female 1 55 15 2 13 4 Search for the loglinear model that can best explain the association patterns in the contingency table by treating (a) smoking and family structure as response variables; (b) smoking as a response variable; and the rest as explanatory variables. For consensus, do not drop any terms with p-value close to but less than 0.05 in model search. In each case, i. State the minimal model. ii. Write down the symbol of the loglinear model that best describes the data and give a step-by-step description of how it was built. iii. Represent the conditional independence structure in the loglinear model using an association graph and explain whether it is a graphical model. Give the symbol of another model that has the same association graph, but is not a graphical model. iv. Explain whether the collapsibility condition can be applied and any conditional inde- pendence structure among variables. Interpret the association between smoking and family structure in the loglinear model. v. Explain whether the zero cell in the contingency table affects your analysis.
Transcribed Image Text:Task 2. The following are data on smoking from a survey of seventh graders (age: 1 = 12 or younger, 2 =13 or older): Smoking Family structure Race Gender Age None Some Black Male 1 2 12 Female 1 2 Both parents White Male 1 394 2 Female 1 21 2237 122 2 4 1 32 19 38 2 94 11 Black Male 1 18 1 2 13 1 Female 1 24 0 2 4 3 Mother only White Male 1 48 6 2 25 4 Female 1 55 15 2 13 4 Search for the loglinear model that can best explain the association patterns in the contingency table by treating (a) smoking and family structure as response variables; (b) smoking as a response variable; and the rest as explanatory variables. For consensus, do not drop any terms with p-value close to but less than 0.05 in model search. In each case, i. State the minimal model. ii. Write down the symbol of the loglinear model that best describes the data and give a step-by-step description of how it was built. iii. Represent the conditional independence structure in the loglinear model using an association graph and explain whether it is a graphical model. Give the symbol of another model that has the same association graph, but is not a graphical model. iv. Explain whether the collapsibility condition can be applied and any conditional inde- pendence structure among variables. Interpret the association between smoking and family structure in the loglinear model. v. Explain whether the zero cell in the contingency table affects your analysis.
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