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Since DDI is bounded between 0 and 1 as earlier mentioned, Papke and Wooldridge (1996) argue that such indices is a fractional/proportional data, and it can be better handled by fractional regression model proposed by the same authors.
Thus, Papke and Wooldridge (1996) proposed Quasi-Maximum Likelihood Estimation (QMLE) to estimate the fractional regression model.5 This model has been widely adopted in similar studies (McDonald 2008; Sauer et al. 2011; Ogundari 2014).
Later, Hoff (2007), McDonald (2009), Banker and Natarajan (2008) and Ramalho et al. (2010) took up the discussion about the use of OLS, Tobit and fractional regression models in the second stage.
Also, using DDS and dietary diversity index (DDI) as additional sets of indicators of food security and zero-truncated Poisson and fractional regression models, we further investigate the determinants of dietary diversity in Nigeria.
In the meantime, QMLE fractional regression employed for the empirical analysis of Eq. 21 when DDI is considered as the dependent variable is specified as: mathrm{E}left left.{mathrm{DDI}}_iright|{Y}_i,{x}_kright)= Gleft({psi}_0+phi {Y}_i+{displaystyle sum_{k=1}^K{beta}_k{x}_{k i}+{eta}_i}right) (26).
Therefore, we employ a multinomial quasi-maximum likelihood fractional regression model that simultaneously investigates the determinants of five hiring alternatives (new trainees, external unskilled staff, external skilled staff with initial vocational education, technicians and master craftsmen, and external staff with higher education).
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The fractional logit regression model is considered a quasi-parametric regression model.
We conducted the meta-regression using linear, first-order, and second-order fractional polynomial regression of the inverse variance weighted data to estimate a best-fitting curve (41).
Fractional logistic regression was used to predict the proportion of fallen trees.
Methods: Linear and fractional polynomial regression analyses were performed with data from a study of Parkinson's disease patients (n=138) to predict the EQ-5D index values from UPDRS and Parkinson's disease questionnaire eight dimensions (PDQ-8) data.
The robust standard errors are given in brackets Table 16 Fractional logit regression with the recovery rate as dependent variable (without censored cases) Variable Recovery rate std.
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