Thursday, October 5, 2017
True composite and factor reliabilities
The menu option “Explore additional coefficients and indices”, available in WarpPLS starting in version 6.0, allows you to obtain an extended set of reliabilities. The extended set of reliabilities includes the classic reliability coefficients already available in the previous version of this software, plus the following, for each latent variable in your model: Dijkstra's PLSc reliability (also available via the new menu option “Explore Dijkstra's consistent PLS outputs”), true composite reliability, and factor reliability. When factor-based PLS algorithms are used in analyses, the true composite reliability and the factor reliability are produced as estimates of the reliabilities of the true composites and factors. They are calculated in the same way as the classic composite reliabilities available from the previous version of this software, but with different loadings. When classic composite-based (i.e., non-factor-based) algorithms are used, both true composites and factors coincide, and are approximated by the composites generated by the software. As such, true composite and factor reliabilities equal the corresponding composite reliabilities whenever composite-based algorithms are used.
Related YouTube video:
Explore True Composite and Factor Reliabilities in WarpPLS
http://youtu.be/DwslOCEvOd4
Fit indices comparing indicator correlation matrices
The new menu option “Explore additional coefficients and indices”, available in WarpPLS starting in version 6.0, allows you to obtain an extended set of model fit and quality indices. The extended set of model fit and quality indices includes the classic indices already available in the previous version of this software, as well as new indices that allow investigators to assess the fit between the model-implied and empirical indicator correlation matrices. These new indices are the standardized root mean squared residual (SRMR), standardized mean absolute residual (SMAR), standardized chi-squared (SChS), standardized threshold difference count ratio (STDCR), and standardized threshold difference sum ratio (STDSR). As with the classic model fit and quality indices, the interpretation of these new indices depends on the goal of the SEM analysis. Since these indices refer to the fit between the model-implied and empirical indicator correlation matrices, they become more meaningful when the goal is to find out whether one model has a better fit with the original data than another, particularly when used in conjunction with the classic indices. When assessing the model fit with the data, several criteria are recommended. These criteria are discussed in the WarpPLS User Manual.
Related YouTube video:
Explore Indicator Correlation Matrix Fit Indices in WarpPLS
http://youtu.be/YutkhEPW-CE
Dijkstra's consistent PLS outputs
The menu option “Explore Dijkstra's consistent PLS outputs”, available in WarpPLS starting in version 6.0, allows you to obtain key outputs generated based on Dijkstra's consistent PLS (a.k.a. PLSc) technique. These outputs include PLSc reliabilities for each latent variable, also referred to as Dijkstra's rho_a's, which appear to be, in many contexts, better approximations of the true reliabilities than the measures usually reported in PLS-based SEM contexts – the composite reliability and Cronbach’s alpha coefficients. Also included in the outputs generated via this menu option are PLSc loadings; along with the corresponding standard errors, one-tailed and two-tailed P values, T ratios, and confidence intervals.
Related YouTube video:
Explore Dijkstra's Consistent PLS Outputs in WarpPLS
http://youtu.be/WdKogy29OVg
Categorical-to-numeric conversion
The menu option “Explore categorical-numeric-categorical conversion”, available in WarpPLS starting in version 6.0, allows you to perform categorical-to-numeric conversions. In a categorical-to-numeric conversion a user can convert a categorical variable, stored as a data label variable, into a numeric variable that is added to the dataset as a new standardized indicator. This new variable can then be used as a new indicator of an existing latent variable, or as a new latent variable with only one-indicator. Three categorical-to-numeric conversion modes, to be used under different circumstances, are available: anchor-factorial with fixed variation, anchor-factorial with variation diffusion, and anchor-factorial with variation sharing.
Related YouTube video:
Explore Categorical-to-Numeric Conversion in WarpPLS
http://youtu.be/XsytZqX7DBc
Numeric-to-categorical conversion
The menu option “Explore categorical-numeric-categorical conversion”, available in WarpPLS starting in version 6.0, allows you to perform numeric-to-categorical conversions. In a numeric-to-categorical conversion one or more of the following are converted into a single data label variable: latent variable, standardized indicator, or unstandardized indicator. This option is useful in multi-group analyses where the investigator wants to employ more than one numeric field for grouping. For example, let us assume that the following two unstandardized indicators are available: C, with the values 1 and 0 referring to individuals from the countries of Brazil and New Zealand; and G, with the values 1 and 0 referring to females and males. By using a numeric-to-categorical conversion a researcher could create a new data label variable to conduct a multi-group analysis based on four groups: “C=1G=1”, “C=1G=0”, “C=0G=1” and “C=0G=0”.
Related YouTube video:
Explore Numeric-to-Categorical Conversion in WarpPLS
http://youtu.be/TWTC-5pqKx8
Reciprocal relationships assessment
Instrumental variables, available in WarpPLS starting in version 6.0, can be used to estimate reciprocal (or non-recursive) relationships. For this, you should use the sub-option “Reciprocal stochastic variation sharing”, under the new menu option “Explore analytic composites and instrumental variables”. To illustrate the sub-option “Reciprocal stochastic variation sharing” let us consider a population model with the following links: A > C, B > D, C > D and D > C. To test the reciprocal relationship between C and D you should first control for endogeneity in C and D, due to variation coming from B and A respectively, by creating two instrumental variables iC and iD via the sub-option “Single stochastic variation sharing” and adding these variables to the model. Next you should create two other instrumental variables through the sub-option “Reciprocal stochastic variation sharing”, which we will call here iCrD and iDrC, referring to the conceptual reciprocal links C > D and D > C respectively. (No links between C and D should be included in the model graph, since reciprocal links cannot be directly represented in this version of this software.) The final model, with all the links, will be as follows: A > C, iC > C, B > D, iD > D, iDrC > D and iCrD > C. Here the link iDrC > D represents the conceptual link C > D, and can be used to test this conceptual link; and the link iCrD > C represents the conceptual link D > C, and can similarly be used to test this conceptual link.
Related YouTube video:
Estimate Reciprocal Relationships in WarpPLS
http://youtu.be/jn8VZaOWe90
Analytic composites and instrumental variables
Analytic composites are weighted aggregations of indicators where the relative weights are set by you, usually based on an existing theory. The menu option “Explore analytic composites and instrumental variables”, available in WarpPLS starting in version 6.0, allows you to create analytic composites. This menu option also allows you to create instrumental variables. Instrumental variables are variables that selectively share variation with other variables, and only with those variables. Instrumental variables can be used to test and control for endogeneity.
Related YouTube videos:
Explore Analytic Composites in WarpPLS
http://youtu.be/bxGi0OY8RD4
Test and Control for Endogeneity in WarpPLS
http://youtu.be/qCvvUxR978U
Multi-group analyses and measurement invariance assessment
The menu options “Explore multi-group analyses” and “Explore measurement invariance”, available in WarpPLS starting in version 6.0, now allow you to conduct analyses where the data is segmented in various groups, all possible combinations of pairs of groups are generated, and each pair of groups is compared. In multi-group analyses normally path coefficients are compared, whereas in measurement invariance assessment the foci of comparison are loadings and/or weights. The grouping variables can be unstandardized indicators, standardized indicators, and labels. These types of analyzes can also be conducted via the new menu option “Explore full latent growth”, which presents several advantages (as discussed in the WarpPLS User Manual).
Related YouTube videos:
Explore Multi-Group Analyses in WarpPLS
http://youtu.be/m2VKQGET-K8
Explore Measurement Invariance in WarpPLS
http://youtu.be/29VqsAjhzqQ
Full latent growth
Sometimes the actual inclusion of moderating variables and corresponding links in a model leads to problems; e.g., increases in collinearity levels, and the emergence of instances of Simpson’s paradox. The menu option “Explore full latent growth”, available in WarpPLS starting in version 6.0, allows you to completely avoid these problems, and estimate the effects of a latent variable or indicator on all of the links in a model (all at once), without actually including the variable in the model. Moreover, growth in coefficients associated with links among different latent variables and between a latent variable and its indicators, can be estimated; allowing for measurement invariance tests applied to loadings and/or weights.
Related YouTube video:
Explore Full Latent Growth in WarpPLS
http://youtu.be/x_2e8DVyRhE
Conditional probabilistic queries
If an analysis suggests that two variables are causally linked, yielding a path coefficient of 0.25 for example, this essentially means in probabilistic terms that an increase in the predictor variable leads to an increase in the conditional probability that the criterion variable will be above a certain value. Yet, conditional probabilities cannot be directly estimated based on path coefficients; and those probabilities may be of interest to both researchers and practitioners. By using the “Explore conditional probabilistic queries” menu option, users of WarpPLS can, starting in version 6.0, estimate conditional probabilities via queries including combinations of latent variables, unstandardized indicators, standardized indicators, relational operators (e.g., > and <=), and logical operators (e.g., & and |).
Related YouTube video:
Explore Conditional Probabilistic Queries in WarpPLS
Sunday, October 1, 2017
Endogeneity assessment and control
Instrumental variables can be used in WarpPLS, starting in version 6.0, to test and control for endogeneity, which occurs when the structural error term for an endogenous variable is correlated with any of the variable’s predictors. For example, let us consider a simple population model with the following links A > B and B > C. This model presents endogeneity with respect to C, because variation flows from A to C via B, leading to a biased estimation of the path for the link B > C via ordinary least squares regression. Adding a link from A to C could be argued as “solving the problem”, but in fact it creates the possibility of a type I error, since the link A > C does not exist at the population level. A more desirable solution to this problem is to create an instrumental variable iC, incorporating only the variation of A that ends up in C and nothing else, and revise the model so that it has the following links: A > B, B > C and iC > C. The link iC > C can be used to test for endogeneity, via its P value and effect size. This link (i.e., iC > C) can also be used to control for endogeneity, thus removing the bias when the path coefficient for the link B > C is estimated via ordinary least squares regression. To create instrumental variables to test and control for endogeneity you should use the sub-option “Single stochastic variation sharing”, under the new menu option “Explore analytic composites and instrumental variables”.
Related YouTube video:
Test and Control for Endogeneity in WarpPLS
http://youtu.be/qCvvUxR978U
Statistical power and minimum sample size requirements
The WarpPLS menu option “Explore statistical power and minimum sample size requirements”, available starting in version 6.0, allows you to obtain estimates of the minimum required sample sizes for empirical studies based on the following model elements: the minimum absolute significant path coefficient in the model (e.g., 0.21), the significance level used for hypothesis testing (e.g., 0.05), and the power level required (e.g., 0.80). Two methods are used to estimate minimum required sample sizes, the inverse square root and gamma-exponential methods. These methods simulate Monte Carlo experiments, and thus produce estimates that are in line with the estimates that would be produced through the Monte Carlo method.
Related YouTube video:
Explore Statistical Power and Minimum Sample Size in WarpPLS
http://youtu.be/mGT6-NKUe3E
Article in the Information Systems Journal discussing the methods:
http://onlinelibrary.wiley.com/doi/10.1111/isj.12131/full
Factor-based SEM
There has been a long and in some instances fairly antagonistic debate among proponents and detractors of the use of Wold’s original partial least squares (PLS) algorithms in the context of structural equation modeling (SEM). This debate has been fueled by one key issue: Wold’s original PLS algorithms do not deal with actual factors, as covariance-based SEM algorithms do; but with composites, which are exact linear combinations of indicators. The factor-based SEM algorithms in WarpPLS have been developed specifically to address this perceived limitation of Wold’s original PLS algorithms.
Related YouTube videos:
Conduct a Factor-Based PLS-SEM Analysis with WarpPLS
http://youtu.be/PvXuD5COezU
Use Consistent PLS Factor-Based Algorithms in WarpPLS
http://youtu.be/I5x4SuQHdME
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