Definitions Flashcards
1-R2 ratio
Diagnostic measure employed in variable clustering to assess whether variables are singularly represented by a cluster component or have a substantive cross-loading
Anti-image correlatoin
Matrix of the partial correlations among variables after factor analysis, representing the degree to which the factors explain each other in the results. The diagonal contains the measure of sampling adequacy for each variable, and the off-diagonal values are partial correlations among variables
a priori criterion
A stopping rule for determining the number of factors. This rule is determined solely on the researcher’s judgment and experience. The researcher may know the desired structure, be testing a specific structure or other conceptually based considerations so that the number of factors can be predetermined
Barlett test of sphericity
Statistical test for the overall significance of all correlations within a correlation matrix
Cluster analysis
Multivariate technique with the objective of grouping respondents or cases with similar profiles on a defined set of characteristics. Similar to Q factor analysis
Cluster component
A principal component extracted in variable clustering which contains only a subset of the complete variable set
Common factor analysis
Factor model in which the factors are based on a reduced correlation matrix. That is communalities are inserted in the diagonal of the correlation matrix, and the extracted factors are based only on the common variance, with specific and error variance excluded
Common variance
Variance shared with other variables in the factor analysis (i.e., shared variance represented by the squared correlation)
Commonality
See communality
Commonulity
Total amount of variance an original variable shares with all other variables included in the factor analysis. Calculated as the sum of the squared loadings for a variable across the factors
Component
See factor
Component analysis
See principial component analysis
Composite measure
See summated scales
Conceptual definition
Specification of the theoretical basis for a concept that is represented by a factor
Confirmatory approach
An approach to factor analysis, typically associated with structural equation modeling, that assesses the extent to which a pre-defined structure fits the data. This approach contrasts with an exploratory approach, which is data driven and the analysis reveals the structure
Convergent validity
The degree to which two measures (scales0 of the same concept are correlated. One aspect of construct validity
Construct validity
Broad approach to ensure the validity of a s et of items as representative of a conceptual definition. Includes specific sub-elements of convergent validity, discriminant validity and nomological validity
Content validity
Assessment of the degree of correspondence between the items selected to constitute a summated scale and its conceptual definition
Correlation matrix
Table showing the intercorrelations among all variables
Cronbach’s alpha
Measure of reliability that ranges from 0 to 1, with values of .60 to .70 deemed the lower limit of acceptability
Cross-loading
A variable has two or more factor loadings exceeding the threshold value deemed necessary for significance in the factor interpretation process
Discriminant validity
One element of construct validity focusing on the degree to which two concepts are distinct. Every scale in the analysis must be shown to have discriminant validity from all other scales
Dummy variable
Binary metric variable used to represent a single category of a nonmetric variable
Eigenvalue
Represents the amount of variance accounted for by a factor. Calculated as the column sum of squared loadings for a factor; also referred to as the latent root
EQUIMAX
One of the orthogonal factor rotation methods that is a “compromise” between the VARIMAX and QUARTIMAX approaches, but is not widely used
Error variance
Variance of a variable due to measurement error (e.g., errors in data collection or measurement)
Exploratory approach
An approach to factor analysis in which the objective is to define the structure within a set of variables, with no pre-specification of number of factors or which variables are part of a factor. Contrasted to a confirmatory approach where the structure is pre-defined
Face validity
See content validity
Factor
Linear combination (variate) of the original variables. Factors also represent the underlying dimension (constructs) that summarize or account for the original set of observed variables
Factor indeterminacy
Characteristic of common factor analysis such that several different factor scores can be calculated for a respondent, each fitting the estimated factor model. It means the factor scores are not unique for each individual
Factor loadings
Correlation between the original variables and the factors, and the key to understanding the nature of a particular factor. Squared factor loadings indicate what percentage of the variance in an original variable is explained by a factor
Factor matrix
Table displaying the factor loadings of all variables on each factor
Factor pattern matrix
One of two factor matrices found in an oblique rotation that is most comparable to the factor matrix in an orthogonal rotation
Factor rotation
Process of manipulation or adjusting the factor axes to achieve a simpler and pragmatically more meaningful factor solution
Factor score
Composite measure created for each observation on each factor extracted in the factor analysis. The factor weights are used in conjunction with the original variable values to calculate each observations score. The factor score then can be used to represent the factor(s) in subsequent analyses. Factor scores are standardized to have a mean of 0 and a standard deviation of 1. Similar in nature to a summated scale
Factor structure matrix
A factor matrix found in an oblique rotation that represents the simple correlations between variables and factors, incorporating the unique variance and the correlations between factors. Most researchers prefer to use the factor pattern matrix when interpreting an oblique solution
Indicator
Single variable used in conjunction with one or more other variables to form a composite measure
Item
See indicator
Kaiser rule
See latent root criterion
Latent root
See eigenvalue
Latent root criterion
One of the stopping rules to determine how many factors to retain in the analysis. In this rule, all factors with eigen values (latent roots) greater than 1.0 are retained
Measure of sampling adequacy (MSA)
Measure calculated both for the entire correlation matrix and each individual variable. MSA values above .50 for either the entire matrix or an individual variable indicate appropriateness for performing factor analysis on the overall set of variables or specific variables respectively
Measurement error
Inaccuracies in measuring the “true” variable values due to the fallibility of the measurement instrument (i.e., inappropriate response scales), data entry errors, or respondent errors. One portion of unique variance
Multicollinearity
Extent to which a variable can be explained by the other variables in the analysis
Nomological validity
An element of construct validity focusing on the extent to which the scale makes accurate predictions of other concepts in a theoretically-based model
Oblique factor rotation
Factor rotation computed so that the extracted factors are correlated. Rather than arbitrarily constraining the factor rotation to an orthogonal solution, the oblique rotation identifies the extent to which each of the factors is correlated
Optimal scaling
Process of transforming nonmetric data (i.e., nominal and ordinal) to a form suitable for use in principal component analysis
Orthogonal
Mathematical independence (no correlation) of factor axes to each other (i.e., at right angles, or 90 degrees)
Orthogonal factor rotation
Factor rotation in which the factors are extracted so that their axes are maintained at 90 degrees. Each factor is independent of, or orthogonal to, all other factors (i.e., correlation between the factors is constrained to be zero)
Parallel analysis
A stopping rule based on comparing the factor eigenvalues to a set of eigenvalues generated from random data. The basic premise is to retain factors that have eigenvalues exceeding those which would be generated by random data.
Percentage of variance criterion
A stopping rule for the number of factors to retain which is based on the amount of total variance accounted for in a set of factors, or the communality of each of the variables. The threshold value is specified by the researcher based on the objectives of the research and judgments about the quality of the data being analyzed.
Principal component analysis
Factor model in which the factors are based on the total variance. With principal component analysis, unities (1s) are used in the diagonal of the correlation matrix; this procedure computationally implies that all the variance is common or shared
Q factor analysis
Forms groups of respondents or cases based on their similarity on a set of characteristics
QUARTIMAX
A type of orthogonal factor rotation method focusing on simplifying the columns of a factor matrix. Generally considered less effective than the VARIMAX rotation
R factor analysis
Analyzes relationships among variables to identify groups of variables forming latent dimensions (factors)
Reliability
Extent to which a variable or set of variables is consistent in what is being measured. If multiple measurements are taken, reliable variables will all be consistent in their values. It differs from validity in that it does not relate to what should be measured, but instead how it is measured
Reverse scoring
Process of reversing the scores of a variable, while retaining the distributional characteristics, to change the relationships (correlations) between two variables. Used in summated scale construction to avoid a canceling out between variables with positive and negative factor loadings on the same factor
Scale development
A specific process, usually involving both exploratory and confirmatory factor analyses, that attempts to define a set of variables which represent a concept that cannot be adequately measured by a single variable
Scoring procedure
Saves the scoring coefficients from the factor matrix and then allows them to be applied to new datasets to generate factor scores as a form of replication of the original results
Scree test
A stopping rule based on the pattern of eigenvalues of the extracted factors. A plot of the eigenvalues is examined to find an “elbow” in the pattern denoting subsequent factors that are not distinctive
Specific variance
Variance of each variable unique to that variable and not explained or associated (correlations) with other variables in the factor analysis. One portion of unique variance
Stopping rule
A criterion for determining the number of factors to retain in the final results, including the latent root criterion, a priori criterion, percentage of variance criterion, scree test and parallel analysis
Summated scales
Method of combining several variables that measure the same concept into a single variable in an attempt to increase the reliability of the measurement. In most instances, the separate variables are summed ant hen their total or average score is used in the analysis
Surrogate variable
Selection of a single proxy variable with the highest factor loading to represent a factor in the data reduction stage instead of using a summated scale or factor score
Trace
Represents the total amount variance on which the factor solution is based. The trace is equal to the number of variables, based on the assumption that the variance in each variable is equal to 1
Unidimensional
A characteristic of the set of variables forming a summated scale where these variables are only correlated with the hypothesized factor (i.e., have a high factor loading only on this factor)
Unique variance
Portion of a variables total variance that is not shared variance (i.e., not correlated with any other variables in the analysis). Has two portions – specific variance relating to the variance of the variable not related to any other variables and error variance attributable to the measurement errors in the variable’s value
Validity
Extent to which a single variable or set of variables (construct validity) correctly represents the concept of study – the degree to which it is free from any systematic or nonrandom error. Validity is concerned with how well the concept is defined by the variable(s), whereas reliability relates to the consistency of the variable(s)
Variable clustering
A variant of principal component analysis which estimates components with only subsets of the original variable set (cluster components). These cluster components are typically estimated in a hierarchical fashion by “splitting” a cluster component when two principal components can be extracted. The splitting process continues until some threshold is achieved
Variate
Linear combination of variables formed by deriving empirical weights applied to a set of variables specified by the researcher
VARIMAX
The most popular orthogonal factor rotation method focusing on simplifying the columns in a factor matrix. Generally considered superior to other orthogonal factor rotation methods in achieving a simplified factor structure.
