TECHNIQUES

MANOVA

Multivariate analysis of variance (MANOVA) is an extension of analysis of variance (ANOVA) methods to cover cases where there is more than one dependent variable and where the dependent variables cannot simply be combined. As well as identifying whether changes in the independent variables have a significant effect on the dependent variables, the technique also seeks to identify the interactions among the independent variables and the association between dependent variables, if any.

Where sums of squares appear in univariate analysis of variance, in multivariate analysis of variance certain positive-definite matrices appear. The diagonal entries are the same kinds of sums of squares that appear in univariate ANOVA. The off-diagonal entries are corresponding sums of products. Under normality assumptions about error distributions, the counterpart of the sum of squares due to error has a Wishart distribution.

Measurement Scales

There are four types of measurements or measurement scales used in statistics. The four types or levels of measurement (nominal, ordinal, interval, and ratio) have different degrees of usefulness in statistical research. Ratio measurements, where both a zero value and distances between different measurements are defined, provide the greatest flexibility in statistical methods that can be used for analysing the data. Interval measurements have meaningful distances between measurements but no meaningful zero value (such as IQ measurements or temperature measurements in degrees Celsius). Ordinal measurements have imprecise differences between consecutive values but a meaningful order to those values. Nominal measurements have no meaningful rank order among values.

 

Multidimensional Scaling

Multidimensional scaling (MDS) is a set of related statistical techniques often used in data visualisation for exploring similarities or dissimilarities in data. MDS is a special case of ordination. An MDS algorithm starts with a matrix of item-item similarities, then assigns a location of each item in a low-dimensional space, suitable for graphing or 3D visualisation.

 

Multinomial Logit Regression

An extension of the binary logit model to cases where the dependent variable has more than 2 categories is the multinomial logit model. In such cases collapsing the data into two categories might not make good sense or may lead to loss in the richness of the data. The multinomial logit model is the appropriate technique in these cases, especially when the dependent variable categories are not ordered (for examples colors like red, blue, green). Some authors have extended multinomial regression to include feature selection/importance methods such as Random Multinomial Logit.