Outliers Analysis

Outliers Analysis

In a multivariate analysis such as Structural equation modeling, the analysis of the outliers have a bigg importance. In fact, univariate outlier is a data point that consists of an extreme value on one variable.  Where multivariate outlier is a combination of unusual scores on at least two variables.  Both types of outliers can influence the outcome of statistical analyses. 

For the analysis of the univariate outliers, was detected using a comparison between 5% trimmed mean, and the mean of the population. In fact, the 5% trimmed mean consist on calculating the mean of the population without taking into consideration the 5% extreme observations. we compare this value to the mean of all the individuals in case there is a significant difference between the two value we suspect the existence of univariate outliers.

In this study and for the three groups (teachers, Students and parents) the difference between the 5% trimmed mean and the mean for the Likert scale variables was between 0.01 and 0.17. This very small difference between the two mean indicate that there is now univariate outlier answer in the data collected. Besides, the Boxplots of all the variables confirms this result (see appendix).

For the analysis of the multivariate outliers, the Mohalanobis distance provides the distance between the each observation and the centroid of all the observations, if this distance is superior to its critical value(  , were p the degree of freedom equals to the number of variables ) the observation is considered as a multivariate outlier. [pic 1]

In our case, and after calculating the Mohalanobis distances, 103 observations were considered as a multivariate outlier, 26 from the student group, 4 from teacher’s group, and 73 from the parents group.  

Parametric Data Assumptions

Structural equation modeling (SEM) has been theoretically and empirically demonstrated to be powerful in disentangling complex causal linkages among variables in social studies, and has become more and more popular in studying the relationships between travel behavior and the built environment. As with other statistical methods, assuming conceptual plausibility, the inferences of causality in the SEM are based on hypothesis tests on the model and the parameter estimates. If the data meet all the assumptions required by an estimation method, the results are assumed to be trustworthy (Univariate normality, multivariate normality, Homoscedasticity, linearity, Multicollinearity, Validity and Reliability).

Normality assumptions:

Table 1: Kolmogorov-Smirnov and Shapiro-wilk’s test

The figures below illustrate the distributions of the variables after the transformation. In fact, we can remark that the reflected logarithm transformation did not show an improvement in the normality of the variables. In addition, referring to Kolmogorov-Smirnov and Shapiro-wilk’s statistics we can reject at 95% of confidence the normality of the transformed variables. Using the Reflected Square transformation the same fact was concluded.

...