Early Television Viewing Is Associated With Protesting Turning Off the Television at Age 6

Dimitri A. Christakis, MD, MPH; Frederick J. Zimmerman, PhD

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In This Article

Modeling

We employed 2 separate analytic approaches to test our hypothesis. First, we ran an ordered logistic regression model to estimate the relationship between our dependent variables and our independent variables. Ordered logistic regression is the best choice of model in a situation such as this in which the outcome variable is categoric; there is a natural ordering among the categories (eg, from best to worst); and the increments between the categories cannot be assumed to represent regular increments in the outcome (ie, in contrast to a count model). In ordered logistic regression the link function is the logistic link, and this is the source of the second part of the name. In addition to estimating the coefficients that are associated with the explanatory variables, one estimates cutpoints that correspond to the thresholds dividing the continuous logistic index function into discrete categories. The probability that the outcome for respondent i will be in a particular category (eg, "almost never," "sometimes," "usually," and "almost always") of N total categories is accordingly represented as:

Pr(outcome i = category 1) = Pr( Xibeta + uic1)

Pr(outcome i = category n) = Pr( cn-1 < Xibeta + uicn), for nsubset{2,3,...,N-1}

Pr(outcome i = category N) = Pr( cN-1 < Xibeta + ui)

in which Xi represents all of patient i's explanatory variables; beta represents the coefficient estimates; and ui is the error term associated with patient i, and the cn are the cutpoints to be estimated. As can be appreciated from this representation, interpretation of the coefficients is challenging. A positive and significant level of a particular coefficient implies that the associated variable has a positive and significant relationship to the outcome.

Ordered logistic regression in this case proffers several advantages. First, it maximizes statistical power. Second, it analyzes the data in the form that they are reported -- as the percentage of respondents who replied in each category. Third, it does not lump cognitively disparate categories into one solely for the purposes of applying logistic regression.

Although ordered logistic regression robustly tests associations, the coefficients are difficult to interpret. We therefore also dichotomized their response to this as "almost never" vs other responses when their children were 6 years of age. This dichotomization was consistent with our sense that such low reported probability of resistance would represent a meaningful outcome from the perspective of parents. The coding of this variable was such that 1 represents protestation and 0 represents no protest.

Regressions incorporated the sampling weights for the child as of the index interview. Given the possibility of multiple children sharing the same mother, we accounted for the potential lack of independence across observations by clustering on the mother's identification number. All analyses were performed in Intercooled Stata 8.0 (Stata Corporation, College Station, Texas).

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