Tablero de Distribución, Equipos de Protección, Control Y Elementos de Conexionado

As mentioned previously, descriptive statistics do not consider the possible interactions taking place between the factors identified as being most likely to increase the risk of workers being poor. To account for those interactions, and because the variable that we are trying to explain is a binary (or dichotomous) variable, a logistic regression model was developed.48

4.3.4.1 Model Specifications

In order to develop a good model, a number of tests were carried out (see Table 4.2). A simple model (Model A) including a constant and a few basic explanatory variables (gender, age and province of residence) was first estimated. Then, groups of explanatory variables were gradually integrated into the model to assess whether or not they added to the model’s predictive power. The ultimate objective was to identify the model that most effectively predicted poverty among workers.

Those tests confirmed that each group of variables that were included in the model enhanced its predictive power. They also allowed us to identify which of the variables did not have a significant impact on the probability of being poor for workers as well as those whose effect was unclear. Ultimately, they led us to make choices relative to the relevance of some explanatory variables.

For example, in Model E, the variables related to the status of full-time/part-time worker and to the status of part-time student were not significant factors in explaining the probability of low income among workers. Accordingly, correlation tests were carried out along with tests to assess whether or not the omission of those variables had a negative impact on the quality of the model.49 Given that the variable concerning a worker’s full-time/part-time status was highly correlated with the variable identifying if workers worked fewer than 1500 hours in 2001, and that its omission did not decrease the model’s predictive power, it was removed from the model. However, since the omission of the variable controlling for part-time student status reduced the model’s predictive power, it was kept.

With respect to the control variables relative to the marital status, they no longer had the expected sign when those relative to the family type were introduced (see Models D and E). Accordingly, correlation tests between marital status and other explanatory variables were carried out. The results of those tests indicated that the variables relative to the status of single and separated/divorced or widowed were too strongly correlated with those relative to the status of unattached individual and lone parent family, which in turn led to overestimating the effects associated with the latter two variables, and made the coefficients associated with the single, separated/divorced or widowed variables negative (and thus counter-intuitive). Given that family type is more important than marital status in explaining poverty among workers, the latter category of variables was omitted from the model.

Finally, despite relatively strong correlations observed between other pairs of variables (such as self-employment and size of business, self-employment and high number of hours of work, or age and experience on the labour market), they were kept in the model given that they control for distinct characteristics.

Table 4.2

Results of the logistic regression models that were tested and of the preferred model, 2001

Models tested A B C D E Preferred model 1. Demographic Characteristics Gender X X X T X T Age T* T* X T* T* T* Province of residence T* T* T* T* T* T* Marital status T T T*_* T*_*

Recent immigrant or Aboriginal person _{T T T T T}

Work limitations _{T T T T T}

2. Socioeconomic Characteristics

Level of education T T T T*

Part-time student _{X X X X}

Experience in the labour market _{T T T T}

3. Family Characteristics

Family type _{T T* T}

4. Characteristics Related to Work Effort

Number of hours worked during the year T T

Main job full-time _X

Only one job during the year _{T T}

5. Characteristics Related to Main Job

Self-employed during the year T

Type of occupation _T*

Size of business _T

Pseudo R2

Area under ROC curve50

2.3 0.615 4.5 0.667 6.6 0.702 14.6 0.783 17.3 0.805 24.1 0.854

The T symbol indicates that it is an explanatory variable included in the model for which each category is

statistically significant at (P<=0.05).

The T* symbol indicates that it is an explanatory variable included in the model for which certain categories are not

statistically significant at (P<=0.05).

The X symbol indicates that it is an explanatory variable included in the model but for which none of the categories

is statistically significant at (P<=0.05).

The T** symbol indicates that it is an explanatory variable included in the model for which all categories are

statistically significant at (P<=0.05) but for which the sign changed with the introduction of new explanatory variables.

Pseudo R2 _{and the area under the ROC curve are two measures of the goodness of fit of the model. In other words,}

they indicate the effectiveness of the regressors included in the model to predict poverty among workers. There is no perfect measure to assess the quality of adjustement of a logistic regression model. It is therefore advisable not to rely on the exact figures obtained through these measures. They can nonetheless be used to check whether or not

any changes to the model will improve the goodness of fit. Pseudo R2 _{is defined as 1-L}

1/L0 where L0 represents the

log of the likelihood of the model with a single constant and L1 the log of the likelihood of the model with the constant

and the other explanatory variables. The more it increases, the better the adjustment of the model is and vice versa. The area under the ROC curve is a more appropriate measure when the actual number of Y=1 in the sample is small (see Appendix C.4 for further explanation). The closer it is to 1, the better the adjustment of the model is and