Factor analysis is a method for investigating whether a number of variables of interest Y1, Y2, ........Yl, are linearly related to a smaller number of unobservable factors F1, F2, ....Fk i.e.; it is a means by which the regularity and order in phenomena can be discerned. As phenomena co-occur in space or in time, they are patterned; as these co-occurring phenomena are independent of each other, there are a number of distinct patterns. Patterned phenomena are the essence of workaday concepts such as "table," "chair," and "house," and--at a less trivial level--patterns structure our scientific theories and hypotheses. We associate a pattern of attitudes, for example, with businessmen and another pattern with farmers.

Factor analysis takes thousands and potentially millions of measurements and qualitative observations and resolves them into distinct patterns of occurrence. It makes explicit and more precise the building of fact-linkages going on continuously in the human mind.

### Types of factor analysis:

**1. ****Confirmatory Factor Analysis**

CFA allows the researcher to test the hypothesis that a relationship between the observed variables and their underlying latent construct(s) exists. The researcher uses knowledge of the theory, empirical research, or both, postulates the relationship pattern a priori and then tests the hypothesis statistically.

The use of CFA could be impacted by the research hypothesis being tested, the requirement of sufficient sample size (e.g., 5-20 cases per parameter estimate), measurement instruments, multivariate normality, parameter identification, outliers, missing data, interpretation of model fit indices etc.

A suggested approach to CFA proceeds through the following process:

· Review the relevant theory and research literature to support model specification

· Specify a model (e.g., diagram, equations)

· Determine model identification (e.g., if unique values can be found for parameter estimation; the number of degrees of freedom, df, for model testing is positive)

· Collect data

· Conduct preliminary descriptive statistical analysis (e.g., scaling, missing data, co linearity issues, outlier detection)

· Estimate parameters in the model

· Assess model fit

· Present and interpret the results.

**1. ****Exploratory Factor Analysis**

It is a variable reduction technique which identifies the number of latent constructs and the underlying factor. It involves the following:

· Hypothesizes an underlying construct, a variable not measured directly.

· Estimates factors which influence responses on observed variables.

· Allows us to describe and identify the number of latent constructs (factors).

· Includes unique factors, error due to unreliability in measurement.

· Traditionally, it has been used to explore the possible underlying factor structure of a set of measured variables.

**Assumptions **underlying EFA are

· Interval or ratio level of measurement

· Random sampling

· Relationship between observed variables is linear

· A normal distribution (each observed variable)

· A bi-variate normal distribution (each pair of observed variables)

· Multivariate normality

**SUGI 31 Statistics and Data Analysis**

**Practical applications in HR:**

HRM practices are analyzed on the basis of recruitment, performance management, reward systems, and retention functions. The HR managers are usually asked to respond to statements such as “Our performance appraisal system is based on results?”,“In determining salaries, offering salaries that are competitive in the job market is more important to our organization than maintaining internal equity,” and “For high level positions the organization prefers to promote personnel from within rather than recruiting personnel from outside the organization.” The items that make up the HRM practices scale are selected from a long list of items, which is done using exploratory factor analysis.

Group- HR1

Author- Tage Otung

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