### Theoretical and Applied Economics

No. 6 / 2008 (523)

## Application of the Model of Principal Components Analysis on Romanian Insurance Market

**Dan Armeanu**

**Leonard Lache**

Academia de Studii Economice, Bucuresti

**Abstract.**
Principal components analysis (PCA) is a multivariate data analysis technique
whose main purpose is to reduce the dimension of the observations and thus simplify the analysis
and interpretation of data, as well as facilitate the construction of predictive models. A rigorous
definition of PCA has been given by Bishop (1995) and it states that PCA is a linear dimensionality
reduction technique, which identifies orthogonal directions of maximum variance in the
original data, and projects the data into a lower-dimensionality space formed of a sub-set of the
highest-variance components. PCA is commonly used in economic research, as well as in other
fields of activity. When faced with the complexity of economic and financial processes, researchers
have to analyze a large number of variables (or indicators), fact which often proves to be
troublesome because it is difficult to collect such a large amount of data and perform calculations
on it. In addition, there is a good chance that the initial data is powerfully correlated; therefore,
the signification of variables is seriously diminished and it is virtually impossible to establish
causal relationships between variables. Researchers thus require a simple, yet powerful annalytical
tool to solve these problems and perform a coherent and conclusive analysis. This tool is PCA.The
essence of PCA consists of transforming the space of the initial data into another space of lower
dimension while maximising the quantity of information recovered from the initial space(1).
Mathematically speaking, PCA is a method of determining a new space (called principal component
space or factor space) onto which the original space of variables can be projected. The axes
of the new space (called factor axes) are defined by the principal components determined as result
of PCA. Principal components (PC) are standardized linear combinations (SLC) of the original
variables and are uncorrelated. Theoretically, the number of PCs equals the number of initial
variables, but the whole point of PCA is to extract as few factors as possible without compromising
the variability of the original space. An important property of the PCs is that the first PC is
extracted so as to recover the variance from the initial space to the maximum possible extent. The
remaining variance is recovered by the next PCs at a declining rate: the variance of the second
PC is greater than the variance of the third PC, the variance of the third PC is greater than the
variance of the fourth PC and so on.

**Keywords: **causal space; principal components; eigen values; variance; insurance; factor matrix; generalized variance.

### Contents

**The epistemic apocalypse**

- Evolution Scenarios at the Romanian Economy Level, Using the R.M. Solow Adjusted Model
Ion Gh. Rosca

Stelian Stancu

- Application of the Model of Principal Components Analysis on Romanian Insurance Market
Dan Armeanu

Leonard Lache

- Aspects Concerning the Optimization of Authentication Process for Distributed Applications
Ion Ivan

Mihai Doinea

Dragos Palaghita

- Planning the Marketing Activity in the Health Care Services
Violeta Radulescu

Iuliana Cetina

Gheorghe Orzan

- The Influence of the Active Rate of Interest over the Financing Decision of the Enterprise
Irena Munteanu

Anca Bran