Time data were transformed into speed (in m/s) by dividing the distance of the travel path over the time taken to complete the travel path. This provided a more normal distribution of these measures. Hence, the ratio of the two speeds, PPWS, was approximately normally distributed.
Descriptive statistics were computed for all the measured variables, including means, standard errors, and range. We plotted PPWS against the vision variables to characterize the relationships between them as part of our model building process. Based on these plots, we introduced spline terms to explore if we could better characterize the respective distributions.
To assess the associations between PPWS and our measured variables, we modeled PPWS as a function of VA, CS, VF, DVA, MT, and MMSE in two stages by using linear regression models. First, we looked at the relationship of each variable to PPWS by using univariate analyses to identify potential covariates. Next, we built the most parsimonious multiple linear regression (MLR) model to predict PPWS. Age, BMI, and race were included in the MLR model, despite nonsignificance in univariate analyses, to account for any variations in the vision variables related to these factors. A 4-m walking speed was also included in the model because of the correlation with PPWS, such that lesser PPWS tended to be observed in conjunction with faster 4-m speeds. By including it, we attempted to ensure that any associations found would reflect relationships of visual impairment with decreased effectiveness in compensating for the increased complexity of the mobility course task and not merely the relationship of visual impairment with slower walking speeds. Having arthritis, having had a stroke, and using a mobility aid were not included in the MLR model, because they were not significantly associated in univariate analyses.
Because we were trying to understand how each vision variable impacted PPWS, we were concerned about multicollinearity among these variables. Therefore, we calculated variance inflation factors (VIF) for all the dependent variables in our MLR model. All VIFs were below 2.0, suggesting little multicollinearity among the variables.
Model diagnostics suggested lesser heteroscedasticity (unequal variance of the error term across observations) when we used the ln PPWS as the outcome variable in our MLR models. However, because this approach did not eliminate heteroscedascity altogether due to the skewed distribution of some of the independent variables, a bootstrapping approach
44 was used to confirm the validity of associations found in our least-squares MLR model. We checked residuals for model fit and were satisfied with the symmetry displayed. The results of our bootstrap regression model concurred with those from the MLR model. Most analyses were carried out with a statistical package (Stata, ver. 7.0; Stata Corp, College Station, TX).