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Review of some Key Latent Variable Principles
Published in Jason T. Newsom, Longitudinal Structural Equation Modeling, 2015
The y* concept is also employed in the context of correlation analysis (Olsson, 1979), where y is conceptualized as a variable that crudely categorizes an otherwise continuous variable. Dichotomization of continuous variables results in an attenuation of the correlation coefficient in comparison to the value of the correlation that would be obtained if the variable had not been dichotomized (Cohen, 1983; Peters & Van Voorhis, 1940). In this sense, the categorized variable can be seen as containing a degree of inaccuracy or error in the measurement of the more precise continuous variable. Special correlation coefficients correct for this attenuation. Tetrachoric (for binary variables), polychoric (for ordinal variables), or polyserial (for binary or ordinal variables mixed with continuous variables) correlations (heretofore all are referred to collectively as “polychoric” correlations) take into account the loss of information when observed binary variables are used as representations of unobserved, continuous, and bivariate normally distributed y* variables. Each is a special case of the general approach.
Developing Item Banks for Patient-Reported Health Outcomes
Published in Steven P. Reise, Dennis A. Revicki, Handbook of Item Response Theory Modeling, 2014
Dennis A. Revicki, Wen-Hung Chen, Carole Tucker
Confirmatory factor analysis (CFA) is recommended to evaluate the extent that the item pool measures a dominant dimension that is consistent with the content experts’ definition of the domain (Reeve et al., 2007). Exploratory factor analysis (EFA) is recommended and is often used as the first step to explore dimensionality. In very specific situations, CFA can be selected as the first step when the pool of items are carefully developed to represent a dominant construct based on an exhaustive literature review and qualitative research. However, in most cases it is advisable to start with EFA to understand potential multidimensionality in the item bank data. Because of the ordinal nature of the patient-reported outcome data, appropriate software (e.g., MPLUS (Muthén & Muthén, 1998) or LISREL (Jöreskog, Sörbom, & Du Toit, 2003)) should evaluate polychoric correlations using an appropriate estimator. Polychoric correlations are used because of the ordinal nature of the data. Recommendations from PROMIS® include weighted least squares with adjustments for the mean and variance estimator in MPLUS or diagonally weighted least squares estimator in LISREL for the confirmatory factor analysis.
Measurement Issues in the Analysis of Within-Person Change
Published in Jason T. Newsom, Richard N. Jones, Scott M. Hofer, Longitudinal Data Analysis, 2013
Daniel E. Bontempo, Frederick M.E. Grouzet, Scott M. Hofer
More recent development of software to estimate polytomous CFA models relaxes the assumption of continuous and normally distributed measures by modeling an LRV underlying each observed polytomous (m-level) measure and estimating a set of m − 1 thresholds connecting the distribution of the LRV to the endorsement frequencies of the m observed response categories under the assumption of multivariate normality (Figure 4.1g). The polychoric correlation of these thresholds permits the application of the usual CFA model using the LRV as continuous measures.* As there is no natural scale for the LRV, their mean and variance are fixed to standard normal (i.e., 0 and 1).
Psychometric Properties of the Spanish Short Version of the Inventory of Personality Organization (IPO-18) in a Nonclinical Sample
Published in Journal of Personality Assessment, 2021
Salvatore Cosentino, Eulàlia Arias-Pujol, Carles Pérez-Testor
The first step of the study was to perform a factorial analysis of the IPO in order to study the latent structure of the Spanish version of the instrument. The latent structure of the IPO was investigated by means of Confirmatory Factor Analysis (CFA) upon the polychoric correlations. Polychoric correlations were used for two reasons. First, the distribution over the response categories was rather skewed for many items, which polychoric correlations can deal with, assuming an underlying normal distribution, and second, no assumptions need to be made regarding the interval scale level of the responses. CFAs were conducted evaluatingtwo different models. The 2-factor (bidimensional) model (the items from “Primitive defenses” and “Identity diffusion” are collected in a single dimension) and the 3-factor solution already known from the original version of the test (this model corresponds to Kernberg’s theory-based separation of Primitive Defenses, Identity Diffusion and Reality Testing impairments) has been tested, to find out if the reduction of items would also lead to a change in the most appropriate factor structure of the instrument.
Gender differences in the associations of early onset poly tobacco and drug use prior to age 18 with the prevalence of adult bronchitis in the United States
Published in Journal of Addictive Diseases, 2020
Muyiwa Ategbole, Brenda Bin Su, Nianyang Wang, Elaine Loudermilk, Xin Xie, Priscila Acevedo, Kaysie Ozuna, Chun Xu, Ying Liu, Kesheng Wang
The SAS PROC SURVEYFREQ was used to weigh and estimate the population prevalence/proportion of bronchitis. The overall prevalence and prevalence of potential factors were estimated. The Chi-square test was used to compare the prevalence of bronchitis across age groups, gender, race, and other factors. Variable cluster analysis in SAS PROC VARCLUS29 was conducted in order to divide nine early onset substance use variables into disjoint clusters. The procedure starts with all variables in one cluster. The chosen cluster is split into two clusters by finding the first two principal components, rotating the components, and assigning each variable to the rotated component with which it has the higher squared correlation. If the second eigenvalue for the cluster is greater than one, the cluster is split into two different dimensions. This procedure finds groups of variables that are as correlated as possible within the cluster and uncorrelated as possible with the variables in other clusters. Considering the categorical variables, the polychoric correlation is applied to ordinal data.30
Nexus of despair: A network analysis of suicidal ideation among veterans
Published in Archives of Suicide Research, 2020
Jeffrey S. Simons, Raluca M. Simons, Kyle J. Walters, Jessica A. Keith, Carol O’Brien, Kate Andal, Scott F. Stoltenberg
We estimated both networks using the R package bootnet (Epskamp et al., 2018) which calls the qgraph package (Epskamp, Cramer, Waldorp, Schmittmann, & Borsboom, 2012). This approach uses the Gaussian Graphical Model to yield pairwise partial correlations between all nodes (Epskamp et al., 2018). Suicidal ideation and childhood trauma were specified as ordinal variables and the remainders were specified as continuous. Thus, polychoric correlations were used as input. The first network has 12 nodes and therefore 66 pairwise associations would be estimated. The second network has 18 nodes and thus, 153 pairwise association parameters would be estimated. However, qgraph uses a graphical LASSO procedure (Tibshirani, 1996) that regularizes the network by identifying only the most relevant edges, thus reducing the number of false positive associations. The LASSO optimizes fit by using the Extended Bayesian information criterion (EBIC) as well as an adjustable hyperparameter (γ). We chose the default value (γ = 0.5) which balances between sparsity and discovery. We used non-parametric bootstrapping to determine significant differences in model edges (Epskamp et al., 2018).