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The results of Table 3 hold when using the linear specification in Eq. 1.
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To check for the consistency of this procedure we compared the results obtained using the linear Blinder - Oaxaca decomposition and the non-linear one (ordered probit specification).
I'm using the linear method".
Because much statistical modeling in epidemiology is performed using some variant of generalized linear models (we used least-squares regression), modelers may assume that the linear specification of these other variables is correct.
Is the linear specification correct, however?
The linear specification of the functional form was rejected for the years 2013 and 2014, while for 2012, it was not possible to detect the missed specification.
The linear specification adopted for the quantile regression may not accommodate non-linear and threshold effects associated with the determinants.
While the linear specification is more common, the log-linear specification can be argued to be more appropriate given that costs are nonnegative and cost distributions typically have long tails.
Since participation in leisure is almost 100%% for either separate or joint leisure together (see Section 3), we can use a linear specification for the leisure equations.
In addition, we tried to operationalize education in various different ways, including International Standard Classification of Education codes and length of education as a continuous variable using both a linear specification and various transformations since a linear relation was not supported by the data.
Instead of a linear model, we carry out the analysis using the nonlinear specification in Eq. 2, where the conditional expectation of the dependent binary variable is a nonlinear function that follows a Probit specification.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com