Factor Analysis In Research Factor analysis is a powerful multivariate statistical technique used to identify underlying relationships between a set of observed variables. By analyzing the intercorrelations among these variables, factor analysis helps researchers determine which variables cluster together to form distinct constructs or factors. This method is particularly useful in elucidating the underlying meaning of complex concepts, especially in fields like nursing research, where it can support instrument development, theory building, and data reduction.
Factor analysis enables researchers to reduce a large number of variables into fewer, manageable factors that can be used to simplify data interpretation. This process is not merely about data reduction; it also provides insights into the structure of the data and can help identify latent variables that may not be directly measurable. As such, factor analysis plays a crucial role in various aspects of nursing research, from evaluating patient outcomes to assessing the effectiveness of interventions.
Types of Factor Analysis
There are two primary types of factor analysis: exploratory factor analysis (EFA) and confirmatory factor analysis (CFA).
Exploratory Factor Analysis (EFA)
Exploratory factor analysis is primarily used in the early stages of research. It allows researchers to explore data without a preconceived notion of the underlying structure. EFA is particularly beneficial when investigating phenomena that are not well-defined or when the researcher seeks to generate hypotheses about the relationships among variables. The goal is to identify potential factors that could explain the observed data patterns.
In EFA, the researcher does not impose a specific structure on the data. Instead, the analysis is data-driven, revealing how variables cluster together and suggesting the presence of latent constructs. EFA is often employed in developing new instruments or scales, as it helps to identify which items should be included based on their correlations.
Confirmatory Factor Analysis (CFA)
Confirmatory factor analysis, on the other hand, is used to test hypotheses or theories about the relationships between observed and latent variables. In CFA, researchers specify a model based on theoretical expectations, and the analysis evaluates how well the observed data fits this model. CFA is typically employed after EFA has been conducted, serving to validate the factor structure identified in the exploratory phase.
In CFA, researchers start with a predetermined number of factors and the expected relationships among them, allowing for a more rigorous testing of theories. This method is especially useful for examining group differences in latent constructs, testing the validity of measurement models, and confirming the dimensionality of scales.
Variables Characteristics
Successful factor analysis requires careful consideration of the characteristics of the variables involved. Several factors influence the validity and reliability of the analysis, including the level of measurement, distribution, and correlation among the variables.
- Level of Measurement: The data should ideally be at the interval level, such as scores obtained from Likert-type scales. This level of measurement ensures that the analysis can accurately reflect the relationships among variables.
- Sample Size: A sufficiently large sample size is crucial to avoid erroneous interpretations of the results. A common rule of thumb is to have at least five cases for each variable, but some researchers suggest that ratios as low as three may be acceptable. However, a sample size of 100 to 200 is generally recommended to ensure robustness in the analysis.
- Distribution of Variables: The variables should be normally distributed, with minimal skewness and kurtosis. This assumption is vital for many statistical methods, including factor analysis, to yield valid results.
- Correlation Structure: Scatterplots should reveal linear relationships between pairs of variables, and significant correlations should exist. Factor analysis is most effective when there are multiple sizable correlations among variables, typically exceeding a threshold of 0.30.
- Outliers: Identifying and managing outliers is critical. Outliers can skew results and lead to misleading interpretations. Researchers should assess the influence of outliers and consider transforming or eliminating them as needed.
- Multicollinearity and Singularity: Researchers must examine the correlation matrix for multicollinearity, where variables are highly correlated, and singularity, where one variable is a linear combination of others. High values in the determinant of the correlation matrix or eigenvalues near zero can indicate these issues.
- Factorability: The correlation matrix should exhibit adequate factorability, which can be assessed through tests such as the Kaiser-Meyer-Olkin (KMO) measure and Bartlett’s test of sphericity.
Considering the Variables
When planning for factor analysis, researchers must establish a theoretical model to guide the process. The choice of psychometric measurement model—either classic or neoclassical—will influence the selection of analytical methods.
Classic vs. Neoclassic Models
- Classic Model: This model assumes that measurement error is entirely random, meaning that all variance is unique to individual variables without shared variance. This simplification can be useful but may overlook systematic errors that can impact the results.
- Neoclassic Model: In contrast, the neoclassic model acknowledges both random and systematic measurement errors. This model allows for the possibility that unmeasured latent factors may contribute to shared variance among observed variables.
Choosing between these models will affect whether the researcher employs principal-components analysis or common factor analysis. The former is typically used to analyze all variance in the variables, while the latter focuses on shared or common factor variance.
Mathematical Description of Analysis
Mathematically, factor analysis generates factors that are linear combinations of the original variables. The first step in factor analysis involves factor extraction, where the goal is to account for as much variance as possible by creating linear combinations that are orthogonal (independent) to one another.
Factor Extraction Methods
- Principal-Components Method: This widely used method extracts all the variance in the dataset and is often employed in exploratory analyses.
- Common Factor Methods: These methods analyze only the variance shared among variables. Common approaches include:
- Principal-Factors Method: Focuses on common variance rather than total variance.
- Maximum Likelihood Method: Utilizes likelihood estimation to determine factor loadings.
Determining the Number of Factors
Various criteria help determine how many factors to retain in an analysis:
- Eigenvalues: One common criterion is to retain factors with eigenvalues greater than 1.0. An eigenvalue represents the amount of variance accounted for by each factor.
- Scree Test: Another approach is the scree test, which involves plotting the eigenvalues and looking for a point where the plot levels off, indicating a natural cutoff for factor retention.
Outcomes of Analysis
Factor extraction yields a factor matrix that illustrates the relationship between observed variables and underlying factors through factor loadings. Factor loadings indicate how much each variable contributes to each factor, and squaring these loadings reveals the variance each factor accounts for.
Communality and Eigenvalues
The sum of squared loadings for a factor provides the communality, which reflects the shared variance among the variables. Each factor’s squared loadings also correspond to its eigenvalue.
Factor Rotation
To facilitate interpretation, researchers often use factor rotation, especially when multiple factors emerge. Rotation helps clarify the relationship between variables and factors by aligning them more clearly.
- Orthogonal Rotation: Keeps the reference axes at right angles, resulting in uncorrelated factors. The most common method is Varimax rotation.
- Oblique Rotation: Allows reference axes to form acute angles, leading to correlated factors. This approach can provide more nuanced insights but also complicates interpretation.
Interpretation of Factors
Once factors are extracted and rotated, researchers interpret them based on the magnitude of the factor loadings. Ideally, some variables will load heavily on a single factor, helping to clarify the factor’s meaning. Generally, loadings of 0.30 and above are considered meaningful.
Factor Scores
After interpreting factors, researchers can calculate factor scores, which provide a numerical representation of each subject’s position on the latent dimension defined by the factor.
Replication and Validation
Replication of factor analyses in different populations strengthens the validity of findings. Comparisons between factor solutions can be conducted through visual inspections or formal statistical methods, enhancing the credibility of the research outcomes.
Conclusion
Factor analysis is a vital tool in nursing research, enabling researchers to uncover underlying constructs and relationships among variables. By employing rigorous methodologies and understanding the nuances of factor analysis, nursing researchers can contribute significantly to theory development, instrument validation, and the overall advancement of nursing science. As the field continues to evolve, factor analysis will remain an essential method for making sense of complex data in healthcare and nursing.