On various causes of improper solutions in maximum likelihood factor analysis

Driel, Van; Otto, Paulo Alberto

doi:10.1007/bf02293865

Cited by 178 publications

(111 citation statements)

References 11 publications

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“…The LISREL program has since been gradually improved (LISREL III: Joreskog & van Thillo 1973;LISREL VII: Joreskog & Sorbom 1987), as regards convenience for the user, additional estimation criteria and model diagnostics. However, one inconvenient side of LISREL, well known to all users, is incurable: LISREL tends to produce improper solutions characterized by negative variance estimates and LV correlations greater than unity (van Driel 1978, Joreskog 1981, Farnell & Bookstein 1982, Rindskopf 1983.…”

Section: Chaptermentioning

confidence: 99%

Latent Variable Path Modeling with Partial Least Squares

Lohmöller

1989

1,459

806

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Section: Chaptermentioning

confidence: 99%

Latent Variable Path Modeling with Partial Least Squares

Lohmöller

1989

1,459

806

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“…Like the cluster and loading recovery, the unique variance recovery depends most on the amount of information; that is, the MAD uniq has a mean value of .22 for the conditions with 20 data blocks or five observations per data block and .05 for the other conditions. Also, the MAD uniq value is affected by the occurrence of Heywood cases (Van Driel, 1978), a common issue in factor analysis pertaining to "improper" factor solutions with at least one unique variance estimated as being negative or equal to zero. When this occurs during the estimation process, LG restricts it to be equal to a very small number (Vermunt & Magidson, 2013).…”

Section: Goodness Of Unique Variance Recoverymentioning

confidence: 99%

“…Specifically, the mean MAD uniq is equal to .18 for the Heywood cases and .04 for the other cases. In the literature, a Heywood case has been considered a diagnostic of problems such as (empirically) underdetermined factors or insufficient sample size (McDonald & Krane, 1979;Rindskopf, 1984;Van Driel, 1978;Velicer & Fava, 1998).…”

Section: Goodness Of Unique Variance Recoverymentioning

confidence: 99%

“…Note that the default random seed is based on time, such that the added random numbers will be unique for each set of starting values (Vermunt & Magidson, 2013). To avoid the occurrence of Heywood cases (Rindskopf, 1984;Van Driel, 1978) very early in the model estimation, the initial unique variances are generated as follows: Preliminary simulation studies indicated a much lower sensitivity to local maxima and a faster computation time when using these starting values instead of mere random values.…”

Section: Multistart Proceduresmentioning

confidence: 99%

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Mixture Simultaneous Factor Analysis for Capturing Differences in Latent Variables Between Higher Level Units of Multilevel Data

Roover

Vermunt

Timmerman

et al. 2017

Structural Equation Modeling: A Multidisciplinary Journal

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Given multivariate data, many research questions pertain to the covariance structure: whether and how the variables (e.g., personality measures) covary. Exploratory factor analysis (EFA) is often used to look for latent variables that might explain the covariances among variables; for example, the Big Five personality structure. In the case of multilevel data, one might wonder whether or not the same covariance (factor) structure holds for each so-called data block (containing data of 1 higher level unit). For instance, is the Big Five personality structure found in each country or do cross-cultural differences exist? The well-known multigroup EFA framework falls short in answering such questions, especially for numerous groups or blocks. We introduce mixture simultaneous factor analysis (MSFA), performing a mixture model clustering of data blocks, based on their factor structure. A simulation study shows excellent results with respect to parameter recovery and an empirical example is included to illustrate the value of MSFA.Keywords: factor analysis, latent variables, mixture model clustering, multilevel data Given multivariate data, researchers often wonder whether the variables covary to some extent and in what way. For instance, in personality psychology, there has been a debate about the structure of personality measures (i.e., the Big Five vs. Big Three debate; De Raad et al., 2010). Similarly, emotion psychologists have discussed intensely whether and how emotions as well as norms for experiencing emotions can be meaningfully organized in a lowdimensional space (e.g., Ekman, 1999;Fontaine, Scherer, Roesch, & Ellsworth, 2007;Russell & Barrett, 1999;Stearns, 1994). Factor analysis (Lawley & Maxwell, 1962) is an important tool in these debates as it explains the covariance structure of the variables by means of a few latent variables, called factors. When the researchers have a priori assumptions on the number and nature of the underlying latent variables, confirmatory factor analysis (CFA) is often used, whereas exploratory factor analysis (EFA) is applied when one has no such assumptions.Research questions about the covariance structure get further ramifications when the data have a multilevel structure; for instance, when personality measures are available for inhabitants from different countries. We refer to data organized according to the higher level units (e.g., the countries) as data blocks. For multilevel data, one can wonder whether or not the same structure holds for each data block. For example, is the Big Five personality structure found in each country or not (De Raad et al., 2010) Setiadi, & Markam, 2002;MacKinnon & Keating, 1989;Rodriguez & Church, 2003).When looking for differences and similarities in covariance structures, using EFA is very advantageous because it leaves more room for finding differences than CFA does. For instance, in the emotion norm example (Eid & Diener, 2001), one might very well expect two latent variables to show up in each country corresponding to approved and disap...

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“…Various causes have been identified that may explain the occurrence of a Heywood case, including outliers (Bollen, 1987), model misspecifications (Kolenikov & Bollen, 2012), and sampling fluctuations (van Driel, 1978). Setting negative variances to zero (or close to zero) is sometimes used as a 'remedy' which can be justified when confidence intervals (CIs) of variance parameters include zero.…”

Section: Admissibility Conditions For Parameter Estimationmentioning

confidence: 99%

Direction of dependence in measurement error models

Wiedermann

Merkle

Eye

2017

Brit J Math & Statis

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Methods to determine the direction of a regression line, that is, to determine the direction of dependence in reversible linear regression models (e.g., x?y vs. y?x), have experienced rapid development within the last decade. However, previous research largely rested on the assumption that the true predictor is measured without measurement error. The present paper extends the direction dependence principle to measurement error models. First, we discuss asymmetric representations of the reliability coefficient in terms of higher moments of variables and the attenuation of skewness and excess kurtosis due to measurement error. Second, we identify conditions where direction dependence decisions are biased due to measurement error and suggest method of moments (MOM) estimation as a remedy. Third, we address data situations in which the true outcome exhibits both regression and measurement error, and propose a sensitivity analysis approach to determining the robustness of direction dependence decisions against unreliably measured outcomes. Monte Carlo simulations were performed to assess the performance of MOM-based direction dependence measures and their robustness to violated measurement error assumptions (i.e., non-independence and non-normality). An empirical example from subjective wellbeing research is presented. The plausibility of model assumptions and links to modern causal inference methods for observational data are discussed.

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On various causes of improper solutions in maximum likelihood factor analysis

Abstract: multivariate analysis, Heywood cases, indefiniteness, interpretability, MALIFA program, sampling, fluctuations,

Cited by 178 publications

References 11 publications

Latent Variable Path Modeling with Partial Least Squares

Latent Variable Path Modeling with Partial Least Squares

Mixture Simultaneous Factor Analysis for Capturing Differences in Latent Variables Between Higher Level Units of Multilevel Data

Direction of dependence in measurement error models

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