Note: Inter-Rater Reliability of Scree Test and Mean Square Ratio Test of Number of Factors

1979 ◽  
Vol 49 (1) ◽  
pp. 223-226 ◽  
Author(s):  
Charles B. Crawford ◽  
Penny Koopman
Keyword(s):  
Correlation Matrix ◽  
Ratio Test ◽  
Mean Square ◽  
Rater Reliability ◽  
Correlation Matrices ◽  
Population Correlation ◽  
Number Of Factors ◽  
Sample Correlation ◽  
The Mean ◽  
Scree Test

The inter-rater reliability of Cattell's scree and Linn's mean square ratio test of the number of factors was studied. Sample correlation matrices were generated from a population correlation matrix by means of standard Monte Carlo procedures such that there were 100 samples based on each of 3 sample sizes. Each matrix was factored and the scree test and the mean square ratio test were each applied by five raters. For both tests, the inter-rater reliabilities were very low. These results suggest that inexperienced factor analysts should be wary of these tests of the number of factors.

scholarly journals Relative Accuracy of Two Modified Parallel Analysis Methods that Use the Proper Reference Distribution

2017 ◽  
Vol 78 (4) ◽  
pp. 589-604 ◽  
Author(s):  
Samuel Green ◽  
Yuning Xu ◽  
Marilyn S. Thompson
Keyword(s):  
Correlation Matrix ◽  
Mean Difference ◽  
Parallel Analysis ◽  
Future Research ◽  
Reference Distribution ◽  
Correlation Matrices ◽  
Number Of Factors ◽  
Distribution Of Eigenvalues ◽  
Sample Correlation ◽  
Comparison Data

Parallel analysis (PA) assesses the number of factors in exploratory factor analysis. Traditionally PA compares the eigenvalues for a sample correlation matrix with the eigenvalues for correlation matrices for 100 comparison datasets generated such that the variables are independent, but this approach uses the wrong reference distribution. The proper reference distribution of eigenvalues assesses the kth factor based on comparison datasets with k−1 underlying factors. Two methods that use the proper reference distribution are revised PA (R-PA) and the comparison data method (CDM). We compare the accuracies of these methods using Monte Carlo methods by manipulating the factor structure, factor loadings, factor correlations, and number of observations. In the 17 conditions in which CDM was more accurate than R-PA, both methods evidenced high accuracies (i.e.,>94.5%). In these conditions, CDM had slightly higher accuracies (mean difference of 1.6%). In contrast, in the remaining 25 conditions, R-PA evidenced higher accuracies (mean difference of 12.1%, and considerably higher for some conditions). We consider these findings in conjunction with previous research investigating PA methods and concluded that R-PA tends to offer somewhat stronger results. Nevertheless, further research is required. Given that both CDM and R-PA involve hypothesis testing, we argue that future research should explore effect size statistics to augment these methods.

scholarly journals Enhancing the Mean Ratio Estimators for Estimating Population Mean Using Non-Conventional Location Parameters

2016 ◽  
Vol 39 (1) ◽  
pp. 63-79 ◽  
Author(s):  
Muhammad Abid ◽  
Nasir Abbas ◽  
Hafiz Zafar Nazir ◽  
Zhengyan Lin
Keyword(s):  
Empirical Study ◽  
Coefficient Of Variation ◽  
Auxiliary Variable ◽  
Mean Square ◽  
Linear Combinations ◽  
Population Correlation ◽  
Location Parameters ◽  
The Mean ◽  
Ratio Estimators ◽  
Mean Square Errors

<p>Conventional measures of location are commonly used to develop ratio estimators. However, in this article, we attempt to use some non-conventional location measures. We have incorporated tri-mean, Hodges-Lehmann, and mid-range of the auxiliary variable for this purpose. To enhance the efficiency of the proposed mean ratio estimators, population correlation coefficient, coefficient of variation and the linear combinations of auxiliary variable have also been exploited. The properties associated with the proposed estimators are evaluated through bias and mean square errors. We also provide an empirical study for illustration and verification.</p>

On Reliability and Number of Principal Components: Joinder with Cliff and Kaiser

1992 ◽  
Vol 75 (3) ◽  
pp. 929-930 ◽  
Author(s):  
Oliver C. S. Tzeng
Keyword(s):  
Principal Component Analysis ◽  
Principal Components ◽  
Correlation Matrix ◽  
Principal Component ◽  
Component Analysis ◽  
Number Of Factors ◽  
Number Of Principal Components ◽  
Scree Test

This note summarizes my remarks on the application of reliability of the principal component and the eigenvalue-greater-than-1 rule for determining the number of factors in principal component analysis of a correlation matrix. Due to the unpredictability and uselessness of the reliability approach and the Kaiser-Guttman rule, research workers are encouraged to use other methods such as the scree test.

Using Results From Replicated Studies to Estimate Linear Models

1992 ◽  
Vol 17 (4) ◽  
pp. 341-362 ◽  
Author(s):  
Betsy Jane Becker
Keyword(s):  
Regression Model ◽  
Spatial Ability ◽  
Random Effects ◽  
Correlation Matrix ◽  
Linear Models ◽  
Random Effects Model ◽  
Average Correlation ◽  
Single Population ◽  
Correlation Matrices ◽  
Population Correlation

This article outlines analyses for the results of a series of studies examining intercorrelations among a set of p + 1 variables. A test of whether a common population correlation matrix underlies the set of empirical results is given. Methods are presented for estimating either a pooled or average correlation matrix, depending on whether the studies appear to arise from a single population. A random effects model provides the basis for estimation and testing when the series of correlation matrices may not share a common population matrix. Finally, I show how a pooled correlation matrix (or average matrix) can be used to estimate the standardized coefficients of a regression model for variables measured in the series of studies. Data from a synthesis of relationships among mathematical, verbal, and spatial ability measures illustrate the procedures.

On the Detection of the Correct Number of Factors in Two-Facet Models by Means of Parallel Analysis

2021 ◽  
pp. 001316442098205
Author(s):  
André Beauducel ◽  
Norbert Hilger
Keyword(s):  
Correlation Matrix ◽  
Full Rank ◽  
Parallel Analysis ◽  
Data Set ◽  
Detection Rates ◽  
Correct Number ◽  
Factor Rotation ◽  
Number Of Factors ◽  
The Mean ◽  
Simulation Results

Methods for optimal factor rotation of two-facet loading matrices have recently been proposed. However, the problem of the correct number of factors to retain for rotation of two-facet loading matrices has rarely been addressed in the context of exploratory factor analysis. Most previous studies were based on the observation that two-facet loading matrices may be rank deficient when the salient loadings of each factor have the same sign. It was shown here that full-rank two-facet loading matrices are, in principle, possible, when some factors have positive and negative salient loadings. Accordingly, the current simulation study on the number of factors to extract for two-facet models was based on rank-deficient and full-rank two-facet population models. The number of factors to extract was estimated from traditional parallel analysis based on the mean of the unreduced eigenvalues as well as from nine other rather traditional versions of parallel analysis (based on the 95th percentile of eigenvalues, based on reduced eigenvalues, based on eigenvalue differences). Parallel analysis based on the mean eigenvalues of the correlation matrix with the squared multiple correlations of each variable with the remaining variables inserted in the main diagonal had the highest detection rates for most of the two-facet factor models. Recommendations for the identification of the correct number of factors are based on the simulation results, on the results of an empirical example data set, and on the conditions for approximately rank-deficient and full-rank two-facet models.

scholarly journals Constructing networks by filtering correlation matrices: a null model approach

2019 ◽  
Vol 475 (2231) ◽  
pp. 20190578
Author(s):  
Sadamori Kojaku ◽  
Naoki Masuda
Keyword(s):  
Correlation Matrix ◽  
Selection Criterion ◽  
Null Model ◽  
Null Models ◽  
Alternative Methods ◽  
Configuration Model ◽  
Correlation Matrices ◽  
Pairwise Correlation ◽  
Country Level ◽  
Sample Correlation

Network analysis has been applied to various correlation matrix data. Thresholding on the value of the pairwise correlation is probably the most straightforward and common method to create a network from a correlation matrix. However, there have been criticisms on this thresholding approach such as an inability to filter out spurious correlations, which have led to proposals of alternative methods to overcome some of the problems. We propose a method to create networks from correlation matrices based on optimization with regularization, where we lay an edge between each pair of nodes if and only if the edge is unexpected from a null model. The proposed algorithm is advantageous in that it can be combined with different types of null models. Moreover, the algorithm can select the most plausible null model from a set of candidate null models using a model selection criterion. For three economic datasets, we find that the configuration model for correlation matrices is often preferred to standard null models. For country-level product export data, the present method better predicts main products exported from countries than sample correlation matrices do.

The Bordeaux Automatic Meridian Circle

1978 ◽  
Vol 48 ◽  
pp. 227-228
Author(s):  
Y. Requième
Keyword(s):  
Mean Square Error ◽  
Mean Square ◽  
Meridian Circle ◽  
The Mean ◽  
Full Automation

In spite of important delays in the initial planning, the full automation of the Bordeaux meridian circle is progressing well and will be ready for regular observations by the middle of the next year. It is expected that the mean square error for one observation will be about ±0.”10 in the two coordinates for declinations up to 87°.

The mean-square generalized delayed decision feedback sequence detector

2003 ◽  
Vol 14 (3) ◽  
pp. 265-268 ◽  
Author(s):  
Maurizio Magarini ◽  
Arnaldo Spalvieri ◽  
Guido Tartara
Keyword(s):  
Decision Feedback ◽  
Mean Square ◽  
The Mean

Limit tolerances for sums of measurement errors

2018 ◽  
Vol 934 (4) ◽  
pp. 59-62
Author(s):  
V.I. Salnikov
Keyword(s):  
Normal Distribution ◽  
Mean Square Error ◽  
Gaussian Distribution ◽  
Measurement Errors ◽  
Theory And Practice ◽  
Mean Square ◽  
The Mean ◽  
Limiting Values ◽  
Limiting Value

The question of calculating the limiting values of residuals in geodesic constructions is considered in the case when the limiting value for measurement errors is assumed equal to 3m, ie ∆рred = 3m, where m is the mean square error of the measurement. Larger errors are rejected. At present, the limiting value for the residual is calculated by the formula 3m√n, where n is the number of measurements. The article draws attention to two contradictions between theory and practice arising from the use of this formula. First, the formula is derived from the classical law of the normal Gaussian distribution, and it is applied to the truncated law of the normal distribution. And, secondly, as shown in [1], when ∆рred = 2m, the sums of errors naturally take the value equal to ?pred, after which the number of errors in the sum starts anew. This article establishes its validity for ∆рred = 3m. A table of comparative values of the tolerances valid and recommended for more stringent ones is given. The article gives a graph of applied and recommended tolerances for ∆рred = 3m.

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