Parental Smoking Behavior, Ethnicity, Gender, and the Cigarette Smoking Behavior of High School Students

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1 Parental Smoking Behavior, Ethnicity, Gender, and the Cigarette Smoking Behavior of High School Students Paul R. Yarnold, Ph.D. Optimal Data Analysis, LLC Novometric analysis is used to predict cigarette smoking (class variable) of 3,577 Anglo-American, 1,001 Mexican-American, and 797 Indian- American (multicategorical attribute) high-school students. Additional categorical attributes used were gender, and dummy-variable indicators of whether the student s mother, and whether the student s father, did or did not smoke. The globally optimal model in this application used only gender as an attribute: moderate ESS=27.1; D=5.4; p< The next more-complex model in the descendant family (moderate ESS=29.7; D= 11.8; p s<0.001) identified five student strata: female Indian-American students had the highest smoking rate (45.6% of 390 students), and male students for whom neither parent smoked had the lowest smoking rate (14.9% of 564 students). Data 1 (Table 1) were originally analyzed using disintegrated chi-square analysis 2 (more modern legacy analyses recommended for this design include the log-linear model 3-10 or logistic regression analysis 3,4,9-17 ), and the findings were reported using undocumented chi-square analysis. 1,18 It was concluded: smoking behavior of children of both sexes for all three ethnic groups reflects that of their parents. For Anglo-American boys the difference between the proportions of smokers when one parent smokes and when neither parent smokes is a significant one (p<0.001). For Anglo-American girls there is a significant difference (p<0.01) in percentages when one parent smokes and when both parents smoke. Mexican-American responses follow the same general pattern: the proportion of smokers is directly related to whether neither, one, or both parents smoke. The same general trend is also found for the Indian-Americans, although no significant differences were noted (pp ). Novometric Statistical Analysis Theoretical and analytic distinctions between novometric vs. alternative methods are detailed elsewhere 10 so the present focus (to the extent it is possible) is on the empirical findings. Table 2 is a summary of the descendant family of optimal models for this application: model four has the lowest D statistic and thus is the globally-optimal (GO) model presently. 136

2 Table 1: Study Data Smoker Ethnicity Mother Father Student Gender N Anglo Yes Yes Yes Male 192 Anglo Yes Yes No Male 503 Anglo Yes No Yes Male 31 Anglo Yes No No Male 85 Anglo No Yes Yes Male 136 Anglo No Yes No Male 413 Anglo No No Yes Male 60 Anglo No No No Male 387 Anglo Yes Yes Yes Female 97 Anglo Yes Yes No Female 520 Anglo Yes No Yes Female 11 Anglo Yes No No Female 91 Anglo No Yes Yes Female 63 Anglo No Yes No Female 563 Anglo No No Yes Female 30 Anglo No No No Female 395 Mexican Yes Yes Yes Male 49 Mexican Yes Yes No Male 106 Mexican Yes No Yes Male 10 Mexican Yes No No Male 22 Mexican No Yes Yes Male 40 Mexican No Yes No Male 131 Mexican No No Yes Male 24 Mexican No No No Male 93 Mexican Yes Yes Yes Female 16 Mexican Yes Yes No Female 153 Mexican Yes No Yes Female 3 Mexican Yes No No Female 28 Mexican No Yes Yes Female 13 Mexican No Yes No Female 197 Mexican No No Yes Female 8 Mexican No No No Female 108 Indian Yes Yes Yes Male 34 Indian Yes Yes No Male 34 Indian Yes No Yes Male 3 Indian Yes No No Male 9 Indian No Yes Yes Male 84 Indian No Yes No Male 97 Indian No No Yes Male 57 Indian No No No Male 72 Indian Yes Yes Yes Female 12 Indian Yes Yes No Female 64 Indian Yes No Yes Female 3 Indian Yes No No Female 10 Indian No Yes Yes Female 19 Indian No Yes No Female 177 Indian No No Yes Female 9 Indian No No No Female 113 Table 2: Descendant Family of Optimal Models Predicting Student Smoking Step ESS Strata Efficiency D Minimum Endpoint N ,672 All of the optimal models had identical performance in training (total sample) and jackknife validity analysis. 9,10 Compared to the GO model the first three models identified in novometric analysis are complex, untenable representations of the antecedents of student smoking. For model 3, for example, increasing the model complexity (number of strata or model endpoints) by 250% (from two to five) yields only an 8.8% [( )/29.7] gain in normed accuracy. The D statistic norms model predictive accuracy for parsimony, and here D indicates that the five-strata model was 2.2-times more distant from a theoretically ideal model having perfect accuracy and maximum possible parsimony for the application. 10,19 GO (Two-Strata) Model The two-strata GO model was: if gender is female, predict non-smoker; otherwise predict smoker (10.5% of females vs. 27.0% of males smoked). Table 3 is the confusion matrix for the model (ESS=27.1, p<0.001), which accurately predicted approximately 1 in 2 of the actual non-smokers (50% accuracy is expected by chance for each class category in two-category applications 9,10 ) compared to 7 in 10 of the actual smokers. Table 3: Confusion Matrix for GO Model Predicted Smoking No Yes Actual No 2,419 1, % Smoking Yes % 137

3 Complex (Five-Strata) Model The five-strata identified are presented below in order from greatest to lowest likelihood of a student being an actual smoker. Greatest likelihood of being a smoker (178/390=45.6%) occurred for female students (gender was the CTA model root attribute) who were of Indian-American descent. Here p<0.001 for all model nodes. 9,10,20-22 The second-greatest likelihood of being a smoker (282/998=28.3%) occurred for males with mothers who smoked. Third-greatest likelihood of a student being a smoker (176/720=24.4%) occurred for males with non-smoking mothers, but with fathers who smoked. The fourth-greatest likelihood of a student being a smoker (542/2282=23.75%) occurred for Anglo-American and Mexican- American females. Finally, lowest likelihood of a student being a smoker (84/564=14.9%) occurred for males for whom neither parent smoked. Table 4 is the confusion matrix for the model (ESS=29.7, all p<0.001), which accurately predicted 2 in 3 of the actual nonsmokers, and 5 in 8 of the actual smokers. Table 4: Confusion Matrix for the Complex Five-Strata Optimal Model Predicted Smoking No Yes Actual No 2,899 1, % Smoking Yes % The set of five student strata identified by the third optimal model in the descendant family yields approximately the same overall level of predictive accuracy normed against chance as does the two-strata GO model. The specific Indian-American female student subtype identified by the more complex model offers more opportunity for intervention than the all males subtype identified by the GO model: 45.6% vs. 27.0% were smokers, respectively. In applications involving risk of adverse events such as adverse drug reactions 23, bioterror 24, criminal recidivism 25 or research confounding 26 for example, complex models while statistically dubious, nevertheless may identify theoretically important and/or pragmatically useful, statistically reliable sample strata: for example, the strata having greatest vs. least need of immediate ( triaged ) intervention. References 1 Zagona SV (1967). Psycho-social correlates of smoking behavior and attitudes for a sample of Anglo-American, Mexican-American, and Indian-American high school students. In: Zagona SV (Ed.), Studies and issues in smoking behavior. Tucson, AZ: University of Arizona Press (pp ). 2 Yarnold PR (2016). CTA vs. disintegrated chisquare: Integrated vs. piecemeal analysis. Optimal Data Analysis, 5, Grimm LG, Yarnold PR (1995). Reading and Understanding Multivariate Statistics. Washington, DC: APA Books. 4 Grimm LG, Yarnold PR (2000). Reading and Understanding More Multivariate Statistics. Washington, DC: APA Books. 5 Yarnold PR (2015). UniODA-based structural decomposition vs. log-linear model: Statics and dynamics of intergenerational class mobility. Optimal Data Analysis, 4, Yarnold PR (2015). Modeling religious mobility by UniODA-based structural decomposition. Optimal Data Analysis, 4, Yarnold PR (2015). UniODA-based structural decomposition vs. legacy linear models: Statics and dynamics of intergenerational occupational mobility. Optimal Data Analysis, 4,

4 8 Yarnold PR (2015). UniODA-based structural decomposition vs. legacy linear models: Statics and dynamics of intergenerational occupational mobility. Optimal Data Analysis, 4, Yarnold PR, Soltysik RC (2005). Optimal data analysis: A guidebook with software for Windows. Washington, DC, APA Books. 10 Yarnold PR, Soltysik RC (2016). Maximizing predictive accuracy. Chicago, IL: ODA Books. DOI: /RG Yarnold PR, Soltysik RC (1991). Refining two-group multivariable classification models using univariate optimal discriminant analysis. Decision Sciences, 22, Yarnold PR, Hart LA, Soltysik RC (1994). Optimizing the classification performance of logistic regression and Fisher s discriminant analyses. Educational and Psychological Measurement, 54, Yarnold PR, Soltysik RC, McCormick WC, Burns R, Lin EHB, Bush T, Martin GJ (1995). Application of multivariable optimal discriminant analysis in general internal medicine. Journal of General Internal Medicine, 10, Yarnold PR, Soltysik RC, Lefevre F, Martin GJ (1998). Predicting in-hospital mortality of patients receiving cardiopulmonary resuscitation: Unit-weighted MultiODA for binary data. Statistics in Medicine, 17, Yarnold PR (2013). Univariate and multivariate analysis of categorical attributes with many response categories. Optimal Data Analysis, 2, Yarnold PR (2014). UniODA vs. logistic regression analysis: Serum cholesterol and coronary heart disease and mortality among middle aged diabetic men. Optimal Data Analysis, 3, Yarnold PR (2015). UniODA vs. logistic regression and Fisher s linear discriminant analysis: Modeling 10-year population change. Optimal Data Analysis, 4, Yarnold PR (2016). ODA vs. undocumented chi-square: Clarity vs. confusion. Optimal Data Analysis, 5, Yarnold PR (2015). Distance from a theoretically ideal statistical classification model defined as the number of additional equivalent effects needed to obtain perfect classification for the sample. Optimal Data Analysis, 4, Yarnold PR (1996). Discriminating geriatric and non-geriatric patients using functional status information: An example of classification tree analysis via UniODA. Educational and Psychological Measurement, 56, Yarnold PR, Soltysik RC, Bennett CL (1997). Predicting in-hospital mortality of patients with AIDS-related Pneumocystis carinii pneumonia: An example of hierarchically optimal classification tree analysis. Statistics in Medicine, 16, Soltysik RC, Yarnold PR (2010). Automated CTA software: Fundamental concepts and control commands. Optimal Data Analysis, 1, Belknap SM, Moore H, Lanzotti SA, Yarnold PR, Getz M, Deitrick DL, Peterson A, Akeson J, Maurer T, Soltysik RC, Storm J (2008). Application of software design principles and debugging methods to an analgesia prescription reduces risk of severe injury from medical use of opioids. Clinical Pharmacology and Therapeutics, 84, Kyriacou DN, Stein AC, Yarnold PR, Courtney DM, Nelson RR, Noskin GA, Handler JA, Frerichs RR (2004). Clinical predictors of bioterrorism-related inhalational anthrax. The Lancet, 364,

5 25 Stalans LJ, Yarnold PR, Seng M, Olson DE, Repp M (2004). Identifying three types of violent offenders and predicting violent recidivism while on probation: A classification tree analysis. Law & Human Behavior, 28, Linden A, Yarnold PR (2016). Using data mining techniques to characterize participation in observational studies. Journal of Evaluation in Clinical Practice. DOI: /jep Author Notes The study analyzed de-individuated data and was exempt from Institutional Review Board review. No conflict of interest was reported. Mail: Optimal Data Analysis, LLC 6348 N. Milwaukee Ave., #163 Chicago, IL