Logistic regression was used to test the hypotheses. Logistical regression allows the prediction of binary outcomes, such as group membership, from a set of independent variables that may include both continuous and indicator variables. One can determine the significance of a logistic regression model by looking at the model chi-square. This indicates whether the overall model is significant. Independent variables are then assessed using the Wald statistic which tests the hypothesis that the coefficient of the independent variable = 0.
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Since the Wald statistic is very hard to interpret, researchers use the odds ratio. The odds ratio represents the change in the likelihood of membership in a target group of a one unit change in the predictor variable. Odds ratios less than one indicate a negative association, or lowered likelihood of group membership. Odds ratios greater than one indicate a positive association, or increased likelihood of membership (Agresti, 1996). For example, suppose we are trying to predict whether a person is male or female where males are coded = 0 and females are coded = 1. An odds ratio of 2.0 for an independent variable indicates that as this independent variable
increases by one unit the person is twice as likely to be female. An odds ratio of .25 would indicate that as the independent variable increased by one unit the person would be .25 as likely to be female (or equivalently 4 times more likely to be male).
For ease of comprehension, researchers frequently do not present the Wald statistics in their output, preferring instead to show the more interpretable odds ratio (labeled ExpB). After presenting the odds ratio in the tables associated with this dissertation I indicate the significance – which is really the statement that the variables’ coefficient is significantly different from zero. For example, the statement: “Hearing impairments were positively associated with being
granted job changes (ExpB 1.764, p <.001)” indicates that the independent variable, job changes, was significantly different from zero using the Wald test. It also indicates that having a hearing impairment makes it 1.764 times more likely that the person received a job change.
In addition to being able to assess the impact of independent variables there are also
measures of overall model fit. One measure of model fit is the Nagelkerke R2. This is a pseudo- R2 measure that indicates the strength of the relationship between the predictors and the
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dependent variable. Unlike OLS regression it is not a measure of variance explained but rather an assessment of how well the model fits. The larger the Nagelkerke the better the model fit.
Regressions were run separately for each of the five categories of accommodation. The control variables (industry and occupation) were entered in the first step of the regression. The second step controlled for three of the four types of predictors being considered (disability related, intersectional, organizational, and institutional). The third step included the predictor variables that were not controlled for in the second step. This process enabled a comparison of the goodness of fit added by each category of predictor. (Note that when running the regressions for “requested accommodation” the sample included only those respondents who reported
needing said accommodation. For “granted accommodation” the sample selected included only those individuals who reported requesting said accommodation.)
In order to interpret the results of the series of hierarchical binary logistical regressions predicting “requesting accommodations”, some further comments on the meaning of Nagelkerke R2 statistics are required. The Nagelkerke score is a pseudo-R2 measure that indicates the
strength of the relationship between predictors and the dependent variable. It represents “an improvement from null model to fitted model. The denominator of the ratio can be thought of as the sum of squared errors from the null model - a model predicting the dependent variable without any independent variables. In the null model, each y value is predicted to be the mean of the y values. The numerator of the ratio would then be the sum of squared errors of the fitted model. The ratio is indicative of the degree to which the model parameters improve upon the prediction of the null model. The smaller this ratio, the greater the improvement and the higher the R-squared.” (UCLA, 2012) "While pseudo R 2s cannot be interpreted independently or
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compared across datasets, they are valid and useful in evaluating multiple models predicting the same outcome on the same dataset. In other words, a pseudo R2 statistic without context has little meaning. A pseudo R2 only has meaning when compared to another pseudo R2 of the same type, on the same data, predicting the same outcome. In this situation, the higher pseudo R2 indicates which model better predicts the outcome." (UCLA, 2011, p.2) As such, while Nagelkerke R² values for each regression model are reported the truly salient findings are the changes in the Nagelkerke values that occur as additional variables are added to each model, representing the improvement in model fit.
To comply with Statistics Canada’s requirements the regressions were weighted so that results accurately reflect the population. The sampling weights are calculated using a three phase process that takes into account sampling design, non-response rates, and post-stratification (which in turn takes into account province, gender, age, and disability severity). For details on the sampling weights see Statistics Canada, 2007. To guard against the possibility of inflating the degrees of freedom in the regression analysis, fractional weights (i.e., sampling weight for the individual ÷ average of all sampling weights) were used. Unweighted analyses showed that the weighting had no effect on the primary conclusions of the study.
6.0 RESULTS
Note: For readability purposes the results associated with “requested accommodations” are presented first in their entirety, followed by the results for “granted accommodations”. Full results tables can be found in Appendix B.
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