1979
DOI: 10.1177/004912417900700405
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Ratio Variables in Aggregate Data Analysis

Abstract: This article discusses three different uses of ratio variables in aggregate data analysis: (1) as measures of theoretical concepts, (2) as a means to control an extraneous factor, and (3) as a correction for heteroscedasticity. In the use of ratios as indices of concepts, a problem can arise if it is regressed on other indices or variables that contain a common component. For example, the relationship between two per capita measures may be confounded with the common population component in each variable. Regar… Show more

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Cited by 50 publications
(5 citation statements)
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“…For this reason, the actual counts of the three types of incidents that occur within each area are retained as measures. To control for the effects of area size and population, these measures are introduced as independent variables in the multiple regression analysis (Agresti and Finlay 1997;Bollen and Ward 1980). 16 …”
mentioning
confidence: 99%
“…For this reason, the actual counts of the three types of incidents that occur within each area are retained as measures. To control for the effects of area size and population, these measures are introduced as independent variables in the multiple regression analysis (Agresti and Finlay 1997;Bollen and Ward 1980). 16 …”
mentioning
confidence: 99%
“…The key problem for aggregate data is that, because the data are aggregated, one cannot reasonably infer the effects of extraneous information or the importance of the information that is lost during aggregation. This point has been made by a number of scholars, including Bollen and Ward (1979), Fox (1984), and Hanushek and Rivkin (2006). Because of this, wide deviations at one level can be rolled up to the next level, and one who sees the final aggregate product will have no knowledge of these deviations.…”
Section: The Issue Of Lists and Public Informationmentioning
confidence: 93%
“…Then, we performed a series of multivariate longitudinal analyses of GRP on RTFs and CFR, adjusting for population and other socioeconomic variables (Bollen and Ward 1979; Schuessl 1974). …”
Section: Methodsmentioning
confidence: 99%
“…Both road safety and socioeconomic variables were entered in the model in their aggregate values. We controlled for population size by including population as a covariate in the regression model to avoid the well-known ratio bias that comes from dividing both dependent and independent variables by population size (Bollen and Ward 1979; Schuessl 1974). Both fixed effects and random effects models were fitted to compare their goodness-of-fit to the panel data for federal regions.…”
Section: Methodsmentioning
confidence: 99%