Questions tagged [confirmatory-factor]

Confirmatory Factor Analysis (CFA) is a set of multivariate techniques aimed at validating the relations between the observed variables, or indicators, and underlying latent variables, or factors, and is typically used to test and describe the underlying structure of psychological scales and other social science measurements.

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Within reverse coding in factor analysis, should the wording of the item itself also be reversed for clarification?

Say for example you have an item that has a negative factor loading, like this: Item 1: I feel emotionally connected with my XBox (-.80) Assume item 1 ranges from 1. Strongly Agree to 7. Strongly ...
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Confirmatory Factor Analysis: Inter-correlation between latent variables vs. cor.test of these latent variables

I am quite inexperienced in the field of statistics and have the following problem. (I work with the statistical software R) I have given students a knowledge test and would like to calculate ...
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Which one first to increase the model fit, set the covariance of two measurement error or delete the items which has low standardized loading?

I see in many references, to increase model fit in CFA, we may set the covariance between the two errors of the observed variables which has high correlation and delete the items that has low ...
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How to calculate categorical omega reliability coefficient when some items only have one value?

From what I understand, running omega reliability in R is quite straightforward, even for binary responses. However, I've encountered a situation when running this command: ...
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How to include observed, exogenous variables in regressions on endogenous latent variables in structural equation models?

Background I'm working with longitudinal survey data collected at two time points. Pre-treatment data were collected, subjects were randomly assigned to a treatment/control group, then post-treatment ...
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How to choose the best converging imputations for my CFA model and pool them

I have 70 imputations of my original data set. I want to choose 50 of them which converged after less than 120 iterations on my CFA model: ...
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When is seemingly unrelated regression equivalent to a confirmatory factor analysis/structural equation model?

One way of describing a seemingly unrelated regression model is: $y_n \sim \beta x_n + \epsilon_j$ where $\epsilon_n \sim MultivariateNormal(0, \Sigma)$. We could rewrite this $y_n \sim MVN(\beta ...
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What's the difference between two correlated variables and two variables with common latent factor?

Is it possible to distinguish two variables that are just correlated with each other but are not part of the same phenomenon, from two variables, that are part of the same phenomenon and share a ...
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Confirmatory factor analysis parameterization of the 2-PL item response model

For binary item response $i$ by person $j$, the 2-PL item response model is of the form: $$Response_{ij} \sim Bernoulli(p_{ij})$$ $$logit(p_{ij}) \sim \alpha_i(\theta_j - \eta_i)$$ Usually, $\alpha_i$ ...
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How to used imputed factor score from AMOS?

I have run two factor CFA (two latent variable with several observed items). My model fit is ok. I have impute factor score and get two imputed scores as I have two latent variable. But I need to ...
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Confirmatory Factor Analysis elimination process

For my thesis, I conducted a survey with 89 questions, resulting in 6 variables in total. The scales I used for the variables are already validated in the literature. Now, I want to find out, which ...
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lavaan warning: The variance-covariance matrix of the estimated parameters (vcov) does not appear to be positive definite

I'm trying to estimate the following CFA model with the lavaan package and get the warning: The variance-covariance matrix of the estimated parameters (vcov) does not appear to be positive definite! ...
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Can you compare a two-factor solution from CFA to a three-factor solution via Chi²-tests?

I got a questionnaire with 30 items and our theory proposes two different factor solutions for this questionnaire. I want to run CFA based on this theory. Solution 1 would include 2 factors on which ...
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Discriminant validity

My question is about the need for this validation. I have highly correlated constructs in a cfa model fitted using the lavaan library in R, so the correlation is greater than the root of the AVE. From ...
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Calculating dof in cfa and sem

I am currently running a cfa and i am unsure which model would be the best to run. I have run one where the factor loadings in all latent variables are equal to one and another model where one of the ...
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Is it correct to calculate Average Variance Extracted (AVE) and Composite Reliability (CR) using loadings from exploratory factor analysis?

In order to obtain evidence of convergence and discriminant validity of a scale, I used SPSS to run a Exploratory Factor Analysis; and used its loadings to calculate the Average Variance Extracted (...
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Comparison indices of CFA

I am comparing different models in Confirmatory Factor Analysis (CFA) to decide what my optimal number of factors and factor structure should be. The main indices I have been using are chi square , ...
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Appropriate statistical model to evaluate the quality of measurements from different instruments?

I have a dataset where a number of samples (>600) were weighed by three different instruments, called V G and P. Each instrument was used three times to weigh each sample so there are nine values ...
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SEM: recursive versus nonrecursive models

Kline (2016) writes on p. 135: There are two kinds of path models. Recursive models are the most straightforward and have two basic features: their disturbances are uncorrelated, and all causal ...
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What is a "method factor" in confirmatory factor analysis and structural equation modeling?

Researchers employing structural equation models and confirmatory factor analyses often choose to include a "method factor" in their models. My understanding is that this is intended to ...
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Discriminant Validity - Chi Square Test

To check discriminant validity between two constructs for CFA in AMOS, I am using chi square difference test to confirm discriminant validity which "can be assessed for two estimated constructs ...
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How to test the significance of contribution of a variable in Factor analysis and what is the resonable rule for removing a variable from FA?

My question is about the credibility from the statistical point of view of what I have seen in some papers where the researchers (non-statistician) define some kind of staged factor analysis (FA) and ...
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Required sample size of CFA using power analysis from semPower

I want to conduct a confirmatory factor analysis (CFA) for a model with 4 latent variables and 60 indicator variables (15 per factor, uncorrelated factors, hence 1,710 degrees of freedom, that is, ...
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Multilevel CFA in R (lavaan); Error: No variance within some clusters

I am running a multilevel CFA in R package lavaan (following the process by Dyer, Hanges, & Hall, 2005). I was able to run an individual-level CFA, and examine both the within group covariance ...
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measurement invariance with many groups

I want to compare how the level of XY (measured using a psychomentric "XY" scale) impacts on the total score of another psychometric instrument (PT score) when controlled for some other ...
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Appropriate standardized solution for a CFA of one latent variable, and multiple ordinal indicators

I am currently working on a CFA in OpenMx, where a standardized latent variable is estimated by multiple ordinal indicators with means and variances restricted to 0 and 1, respectively. According to ...
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Is it necessary to do a second order CFA to create a total score summing across factors?

I am in the process of developing a scale. I have already performed EFA on the first dataset I collected, which showed strong support for a 4 factor structure. I am now planning to collect another ...
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Scale development

I am in the process of developing a scale that is supposed to measure construct X with 4 factors. I have already found support for a 4-factor model to the data using exploratory factor analysis. Now, ...
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Why standardized factor loading > 1 ? (CFA in lavaan)

I am runing CFA in R with the lavaan package. My model is one factor with 5 variales. I set std.lv = TRUE, but the estimated factor loading is still > 1. Can I report the std.all column as my ...
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Which model fit indices do you report from lavaan cfa for scale development?

For RMSEA there seems to be a regular value and two robust values. Are there any recommendations on which of the three values to report? Would you report 1, 2 or 3 from lavaan?
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Why don't I have metric measurement invariance even with very small differences between factor loadings across groups?

Background: I'm running a multi-group model in lavaan. It has two groups: One clinical sample (n = 160) and one healthy control sample (n = 248) that I chose to be comparable regarding age, gender and ...
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Bifactor model. Specific factor collapsed and shifted

I ran a bifactor model and there was a strongly defined general factor and appreciable leftover variance for specific factor A but not specific factor B. When I removed one item that loaded poorly to ...
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Estimated covariance matrix and sample covariance matrix of SEM

Normal Covariance I have tried looking high and low for an answer to this question, but I seem to never get a great answer on it. First, I think I'm knowledgeable about what a covariance matrix is. It ...
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Chi-Square Tests with MLE in Confirmatory Factor Analysis

I have a basic question about confirmatory factor analysis. When performing CFA, Chi-square test is often used. I read from the book that after using MLE for factor extraction (computing covariance ...
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what are the right or common steps to successfully build a structural equation model?

I have learned theories about structural equation modeling but don't have enough experience building a structural equation model. I have spent too much time struggling with building a good SEM. I have ...
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Justify the deletion of a factor in EFA

I have done an EFA on 180 observations. In order to explain my latent variables I have considered 24 variables and I get 7 factors. Unfortunately 2 factors among the 7 have a cronbach's alpha around 0....
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sumscores instead of factorscores or SEM

Suppose I would like to use sumscores after running a confirmatory factor analysis (CFA) with two latent factors. The items for each factor are then summed and in subsequent analyses these sums are ...
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Within ML CFA with categorical data (polychoric correlation), are there not different thresholds for both the within and between level?

I am currently studying multilevel confirmatory factor models of categorical data. In the context of CFAs, categorical data is often analysed through polychoric correlations. Within polychoric ...
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Confirmatory Factor Analysis (CFA) for nested data

I would like to conduct CFA to examine support for a 3-factor model with team_cohesion, team_trust, and team_performance variables. I have the data in the following format with individuals rating the ...
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Bifactor Model in R: High factor loadings but non-significant p-values

I'm currently running an bifactor model (R - lvaan) with one general factor and three domain specific factors (X1, X2, X3). The dataset contains 18 items, of which it is assumed in theory that six ...
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The scale I am developing for a main study has partial metric and partial scale invariance. Can I still use this in my study?

I'm developing a scale that will be later used in a main study. This study will take place in the UK and France. The scale itself consists of 9 items. I initially tested the scale in UK participants ...
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Preparing Likert Data for CFA

I've been running a CFA on Likert scale data that averages the responses for each item, and I've been thinking that if I could possibly run the analysis without averaging the responses, it might ...
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Fix second-order factor loadings to equal in all second-order factors with two first-order factor indicators? CFA / SEM

I am conducting a CFA followed up by a SEM analysis. In my original model I had 13 latent variables. As some of these were highly correlated, I created second-order factors, of which 3 are indicated ...
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How to model an interacton between a categorical IV and a continous moderator (created through a CFA) in a SEM model using the lavaan package in R?

How can one go about modelling the interaction between a categorical independent variable and a continous moderator (created through a CFA) in a SEM model using the lavaan package in R? In particular, ...
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Confirmatory Factor Analysis identifying

I have been explained this technique in class. However, I did not understand some stuff. The professor said that a model to be estimated needs to be at least identified. Identified meaning to be when ...
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factor score formula in lavaan

I would like get the factor scores of R/lavaan, achieved by a CFA model (single factor, 4 continuous indicators), by hand. Which is the formula (equation) as function of the observed indicators. In ...
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SEM with nonnormal latent variables

From my reading of the structural equation modeling (SEM) literature, multivariate normality (MVN) is typically discussed with regards to the indicator variables (i.e., items). I am interested in ...
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How to Assess Standardized Factor Loading

I'm running a CFA in lavaan, and I understand that as a general rule of thumb, each item should have a standardized loading on the factor of <|0.3|. I've been making the mistake of reviewing the ...
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Why set factor means to 0? Monte Carlo simulation

I am using structural equation modeling (SEM). My model is a simple mediation model with latent variables (each latent variable has 3 indicators). I want to run a Monte Carlo simulation to estimate if ...
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CFA model interpretation

I received the following CFA model output. I wonder if anyone can help me understand how to interpret values on each path. For example, in factor 3, what does 1, 0.535, and p-value mean? I know that ...
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