Regression Technique Sample Clauses

Regression Technique. Regression was performed with the goal to be able to look at the direction and size of the influence of certain variables. The exact model that was performed, is called the Ordinal Logistic Regression (OLR) model. This model was chosen because the logistic function can be used to model the odds of the three discrete outcomes (-1, 0, 1) as a linear combination of the independent variables. One could argue that a multinomial logit model would also be suitable, but this model does not take into account that our dependent variable is ordinal. Thus, the ordinal logit model fulfils both the ordinality and discreteness requirements and can produce probability estimates for such outcomes (Xxxxxxxx & XxxXxxxxx, 2004). The fundamentals of the model will now be elaborated upon, using the research of Xxxxx and Xxxxxxxxx (2013). The ordinal logit model tries to create a connection between the independent variables (i.e. the features) and a discrete dependent variable by means of an unobservable continuous dependent variable. The connection is achieved by assuming that the continuous variable is a function of the independent variables and a disturbance (or randomness) with known distribution properties. Each value of this continuous dependent variable relates to a set of probabilities for each possible value of the discrete dependent variable. For each part of the model, some assumptions need to be made. For the disturbance, a standardized logistic distribution is assumed. This is a symmetric distribution similar to the normal distribution. Concerning the independent variables, it is assumed that a linear relationship exists between them and the unobservable continuous variable. To be more exact, the unobservable continuous variable is the sum of the disturbance and the product of the independent variables with an equally long vector of constants. Mathematically, this can be written as: 𝑦∗ = 𝜷𝑻𝑿 + 𝜀, with 𝑦∗ the unobservable continuous variable, 𝑿 a vector of n independent variables and 𝜷𝑻 a vector of n constants (Davidson & XxxXxxxxx, 2004). Finally, the relation between the unobservable continuous variable 𝑦∗ and the observable discrete variable y is assumed by giving 𝑦∗ some constant threshold points 𝜅̂𝑘. The value of y then depends on whether 𝑦∗ has crossed a particular threshold. Thus, the probability of observing a certain state of the discrete dependent variable y depends on 𝜷𝑻𝑿 and the constant threshold values 𝜅̂𝑘. As the expression of these ...