A protocol for modelling generalised biological responses using latent variables in structural equation models

Lamb, E. G., Shirtliffe, S. J. and May, W. E. 2011. Structural equation modeling in the plant sciences: An example using yield components in oat. Can. J. Plant Sci. 91: 603-619. Structural equation modeling (SEM) is a powerful statistical approach for the analysis of complex intercorrelated data with a wide range of potential applications in the plant sciences. In this paper we introduce plant scientists to the principles and practice of SEM using as an example an agronomic field trial. We briefly review the history of SEM and path analysis and introduce the statistical concepts underlying SEM. We demonstrate the use of observed and latent variable structural equation models using a multi-site multi-year field trial examining the effects of seed size and seeding density on the plant density and yield of oat in Saskatchewan. Using SEM allowed for insights that a standard univariate analysis would not have revealed. We show that seeding density has strong effects on plant and panicle density, but has very limited effects on final yield. Plant density has a consistent non-linear effect on panicle density across location that was not affected by precipitation. In contrast, the implicit effect of precipitation on seed number appears to be the main driver for final yield. Incorporating precipitation data into the model demonstrates how mechanistic models can be developed by including in the path diagram variables that would normally treated as random factors in a mixed model analysis. Finally, we provide a guideline to assist plant scientists in determining whether SEM is an appropriate method to be used for the analysis of their data.

Purpose: Since oxidative stress involves a variety of cellular changes, no single biomarker can serve as a complete measure of this complex biological process. The analytic technique of structural equation modeling (SEM) provides a possible solution to this problem by modelling a latent (unobserved) variable constructed from the covariance of multiple biomarkers.Methods: Using three pooled datasets, we modelled a latent oxidative stress variable from five biomarkers related to oxidative stress: F2-isoprostanes (FIP), fluorescent oxidation products, mitochondrial DNA copy number, γ-tocopherol (Gtoc) and C-reactive protein (CRP, an inflammation marker closely linked to oxidative stress). We validated the latent variable by assessing its relation to pro- and anti-oxidant exposures.Results: FIP, Gtoc and CRP characterized the latent oxidative stress variable. Obesity, smoking, aspirin use and β-carotene were statistically significantly associated with oxidative stress in the theorized directions; the same exposures were weakly and inconsistently associated with the individual biomarkers.Conclusions: Our results suggest that using SEM with latent variables decreases the biomarker-specific variability, and may produce a better measure of oxidative stress than do single variables. This methodology can be applied to similar areas of research in which a single biomarker is not sufficient to fully describe a complex biological phenomenon.

Calls for accountability, coupled with a desire to improve teaching and learning, have prompted many colleges and universities to consider ways of assessing the effects of postsecondary education on student growth and development. Despite widespread support for the concept of assessing student change, relatively few institutions have implemented this type of assessment, in part because of a concern about the best method of measuring change. This article describes the use of structural equation models with latent variables to assess the effects of education on change. Advantages of using structural equation models with latent variables include error-free measurement of change, direct tests of the assumptions underlying change research, along with the power and flexibility of maximum likelihood estimation. An analysis of data on freshman-to-senior gains provides evidence of the advantages of latent variable structural equation modeling and also suggests that the group differences identified by traditional analysis of variance and covariance techniques may be an artifact of measurement error.

The foundations of structural equation modeling started with Spearman's attempt to identify different dimensions of intelligence in order to generate an overall general intelligence factor. Kline simplified the categorization of SEM techniques by stating that, historically, factor analysis deals with measurement, path analysis assesses structure, and latent growth modeling deals with changes over time. Before the various types of structural equation models are discussed, it would be useful to review a list of common terms found in the SEM literature. Latent variable structural equation models are causal models that include latent variables. At the time that this chapter was written, there was limited research using SEM techniques with large scale quantitized text data. Kline is one of the more widely used for an introduction to structural equation modeling and it is not software specific.

BackgroundCulture-independent phylogenetic analysis of 16S ribosomal RNA (rRNA) gene sequences has emerged as an incisive method of profiling bacteria present in a specimen. Currently, multiple techniques are available to enumerate the abundance of bacterial taxa in specimens, including the Sanger sequencing, the ‘next generation’ pyrosequencing, microarrays, quantitative PCR, and the rapidly emerging, third generation sequencing, and fourth generation sequencing methods. An efficient statistical tool is in urgent need for the followings tasks: (1) to compare the agreement between these measurement platforms, (2) to select the most reliable platform(s), and (3) to combine different platforms of complementary strengths, for a unified analysis.ResultsWe present the latent variable structural equation modeling (SEM) as a novel statistical application for the comparative analysis of measurement platforms. The latent variable SEM model treats the true (unknown) relative frequency of a given bacterial taxon in a specimen as the latent (unobserved) variable and estimates the reliabilities of, and similarities between, different measurement platforms, and subsequently weighs those measurements optimally for a unified analysis of the microbiome composition. The latent variable SEM contains the repeated measures ANOVA (both the univariate and the multivariate models) as special cases and, as a more general and realistic modeling approach, yields superior goodness-of-fit and more reliable analysis results, as demonstrated by a microbiome study of the human inflammatory bowel diseases.ConclusionsGiven the rapid evolution of modern biotechnologies, the measurement platform comparison, selection and combination tasks are here to stay and to grow – and the latent variable SEM method is readily applicable to any other biological settings, aside from the microbiome study presented here.

The Development of the RAM Rules for Latent Variable Structural Equation Modeling

Cross-sectional. To develop a latent structural model to demonstrate the relationship between factor structures of protective health behaviors and pressure ulcer (PrU) outcomes among participants with spinal cord injury (SCI). Data were collected at a large specialty hospital and analyzed at a medical university in the Southeastern USA. A total of 1871 participants with traumatic SCI of at least 1 year duration were included. A latent PrU variable was measured by four observable PrU-related outcomes. Latent variable structural equation modeling was performed to assess the relationship between latent protective behavior (fitness and productive activities) and latent PrU outcome. Several exogenous variables were included: sex, age, race, marital status, injury severity and years since injury. The protective behavior dimension had a significant direct effect on the latent PrU (direct effect=-0.275, P<0.01). All direct relationships between protective behavior dimension and healthy behaviors were also significant (rfit=0.899 and rproductive activity=0.568). Relationships between the latent PrU and fitness (indirect effect=-0.247) and productive activities (indirect effect=-0.156) were mediated through the protective behavior dimension. Participants who were African American, had higher injury levels, and had longer time since SCI were more likely to have worse PrU outcomes. The overall findings of this study suggest the need to enhance healthy behaviors to prevent adverse PrU outcomes, especially among people who are African American, have longer time since SCI and have higher level of SCI.

Petrinovich highlighted many salient issues in the behavioral and social sciences that are of concern to this day, such as insufficient attention to construct validity. Structural equation modeling, particularly with regard to latent variables, is introduced and discussed in this context. Though conceptual issues remain, analytic and statistical techniques have made immense strides in the past three decades since the article was written, and properly used, offer solutions to many problems Petrinovich identified.

This article illustrates the use of structural equation modeling (SEM) procedures with latent variables to analyze data from experimental studies. These procedures allow the researcher to remove the biasing effects of random and correlated measurement error on the outcomes of the experiment and to examine processes that may account for changes in the outcome variables that are observed. Analyses of data from a Project Family study, an experimental intervention project with rural families that strives to improve parenting skills, are presented to illustrate the use of these modeling procedures. Issues that arise in applying SEM procedures, such as sample size and distributional characteristics of the measures, are discussed.

Structural Equation Modeling with latent variables (SEM) is a powerful tool for social and behavioral scientists, combining many of the strengths of psychometrics and econometrics into a single framework. The most common estimator for SEM is the full-information maximum likelihood estimator (ML), but there is continuing interest in limited information estimators because of their distributional robustness and their greater resistance to structural specification errors. However, the literature discussing model fit for limited information estimators for latent variable models is sparse compared to that for full information estimators. We address this shortcoming by providing several specification tests based on the 2SLS estimator for latent variable structural equation models developed by Bollen (1996). We explain how these tests can be used to not only identify a misspecified model, but to help diagnose the source of misspecification within a model. We present and discuss results from a Monte Carlo experiment designed to evaluate the finite sample properties of these tests. Our findings suggest that the 2SLS tests successfully identify most misspecified models, even those with modest misspecification, and that they provide researchers with information that can help diagnose the source of misspecification.

Concepts associated with latent variables What is a latent variable? As indicated in our overview of structural equation models at the beginning of Chapter 3, in addition to observed variables in structural equation models, another type of variable, referred to as a latent variable, is commonly included. There are a variety of ways latent variables can be defined. Strictly speaking, a latent variable is one that is hypothesized to exist, but that has not been measured directly. Bollen (2002) states that we can simply think of a latent variable as one that is unobserved. In spite of this simple definition, latent variables are typically used to represent concepts. However, there are many types of concept and not all of them correspond to latent variables. Further, the algorithms used to calculate latent variables define their quantitative properties, although how they are interpreted is a matter of theoretical consideration. Finally, latent variables are starting to be used in structural equation models for a wider variety of purposes, such as to represent parameters in latent growth modeling. Because latent variables are often used to represent abstractions, their meaning is not always immediately obvious. For this reason, I believe it will be best to rely on a variety of examples and a discussion of their properties to illustrate the roles latent variables can play in SEM.

In debates over the roles of law and government in promoting the equality of income or in redistributing the fruits of capitalism, widely different motives are attributed to those who favor or oppose capitalism or income redistribution. According to one view, largely accepted in the academic social psychology literature (Jost et al. 2003), opposition to income redistribution and support for capitalism reflect an orientation toward social dominance, a desire to dominate other groups. According to another view that goes back at least to the nineteenth century origins of Marxism, anti-capitalism and a support for greater legal efforts to redistribute income reflect envy for the property of others and a frustration with one’s lot in a capitalist system. In this paper I expand and test the social dominance thesis using sixteen nationally representative General Social Surveys conducted by the National Opinion Research Center between 1980 and 2004. Because few questions of interest were asked in most years or of most respondents, the sample sizes used for analyses vary from 535 to 15,743. I first show that respondents who express traditionally racist views (on segregation, interracial marriage, and inborn racial abilities) tend to support greater income redistribution. Traditional racists also tend to oppose free-market capitalism and its consequences, wanting the government to guarantee jobs for everyone and fix prices, wages, and profits. Next, I report a similar pattern for those who express intolerance for unpopular groups on the fifteen Stouffer tolerance questions (regarding racists, homosexuals, communists, extreme militarists, and atheists). Those who express less tolerance for unpopular groups tend to favor income redistribution and oppose capitalism. Then I present the results of six full latent variable structural equation models. The latent variables traditional racism (Model 1: r=.27) and intolerance (Model 2: r=.31) predict the latent variable income redistribution. Similarly, the latent variables traditional racism (Model 3: r=.33) and intolerance (Model 4: r=.36) predict anti-capitalism. Controlling for education, income (log), gender, and age (Models 5 and 6), the effects of the racism and intolerance predictors on redistribution and intolerance are reduced, but remain significant. Thus the preference against income redistribution, for example, is not just the result of income or education - rather, the data are consistent with racism and intolerance continuing to play a small, but significant role in explaining the support for income redistribution and anti-capitalism. The data are broadly inconsistent with the standard belief in the social psychology literature that pro-capitalist and anti-redistributionist views are positively associated with racism. I then explore an alternative hypothesis, showing that, compared to anti-redistributionists, strong redistributionists have about two to three times higher odds of reporting that in the prior seven days they were angry, mad at someone, outraged, sad, lonely, and had trouble shaking the blues. Similarly, anti-redistributionists had about two to four times higher odds of reporting being happy or at ease. Not only do redistributionists report more anger, but they report that their anger lasts longer. When asked about the last time they were angry, strong redistributionists were more than twice as likely as strong opponents of leveling to admit that they responded to their anger by plotting revenge. Last, both redistributionists and anti-capitalists expressed lower overall happiness, less happy marriages, and lower satisfaction with their financial situations and with their jobs or housework. Further, in the 2002 and 2004 General Social Surveys anti-redistributionists were generally more likely to report altruistic behavior. In particular, those who opposed more government redistribution of income were much more likely to donate money to charities, religious organizations, and political candidates. The one sort of altruistic behavior that the redistributionists were more likely to engage in was giving money to a homeless person on the street. Evidence from sixteen national representative samples from 1980 through 2004 tends to suggest that Social Dominance Orientation has been in part misconceived. In the United States, segments of the academic community seem to have reversed the relationship between pro-capitalism and income redistribution on the one hand, and racism and intolerance on the other. Those who support capitalism and oppose greater income redistribution tend to be better educated, to have higher family incomes, to be less traditionally racist, and to be less intolerant of unpopular groups. Those who oppose greater redistribution also tend to be more generous in donating to charities and more likely to engage in some other altruistic behavior. The academic assumption that anti-capitalism and opposition to income redistribution reflect an orientation toward social dominance seems unwarranted.

Anti-transgender policies and state legislative initiatives that focus on school bathroom use and hormone use have emerged in recent years. These policies are generally written by and voted on by cisgender people, and as such, it is crucial to understand influences on nonaffirming attitudes toward policies that can impact trans youth. The present study aimed to extend research on transphobic attitudes in general to attitudes toward policies that impact youth undergoing transition. Latent variable covariances and structural equation modeling were used to test the relations between transphobia, genderism, homophobia, need for closure, sexual orientation, social dominance orientation, attitudes toward sexual minorities, beliefs about gender roles, aggression, religious fundamentalism, and contact with sexual and gender minority individuals, as they are related to attitudes toward hormone use and bathroom use for trans youth. Analyses of data from a sample of 248 cisgender adults indicated that genderism and transphobia was associated with attitudes toward gender-affirming hormone use and bathroom use for trans youth; need for closure was associated with gender-affirming attitudes toward bathroom use, but was not associated with hormone use. Sexual orientation was linked to attitudes toward gender-affirming policies, such that nonheterosexual participants had more affirming attitudes toward trans youths' bathroom use, but not hormone use. Implications for future research, advocacy efforts to promote rights for trans youth, and clinical work with trans youth and/or parents/guardians of trans youth are discussed. (PsycInfo Database Record (c) 2022 APA, all rights reserved).

This article discusses several advantages of latent variable structural equation modeling (LVSEM), and the potential it has for solving some fundamental problems hindering research in the field. The advantages highlighted include the ability to control for measurement error; an enhanced ability to test the effects of experimental manipulations; the ability to test complex theoretical structures; the ability to link micro and macro perspectives; and more powerful ways to assess measure reliability and validity. My hope is to sensitize researchers to some of the key limitations of currently used alternative methodologies, and demonstrate how LVSEM can help to improve theory testing and development in our discipline.

The interaction between positive, negative and depressive symptoms experienced by people with schizophrenia is complex. We used longitudinal data to test the hypothesis that depressive symptoms mediate the links between positive and negative symptoms. We analyzed data from the European Schizophrenia Cohort, randomly sampled from outpatient services in France, Germany and the UK (N = 1208). Initial measures were repeated after 6 and 12 months. Depressive symptoms were identified using the Calgary Depression Scale for Schizophrenia (CDSS), while positive and negative symptoms were assessed with the Positive and Negative Syndrome Scale (PANSS). Latent variable structural equation modelling was used to investigate the mediating role of depression assessed at 6 months in relation to the longitudinal association between positive symptoms at baseline and negative symptoms at 12 months. We found longitudinal associations between positive symptoms at baseline and negative symptoms at 12 months, as well as between both of these and CDSS levels at 6 months. However depression did not mediate the longitudinal association between PANSS scores; all the effect was direct. Our findings are incompatible with a mediating function for depression on the pathway from positive to negative symptoms, at least on this timescale. The role of depression in schizophrenic disorders remains a challenge for categorical and hierarchical diagnostic systems alike. Future research should analyze specific domains of both depressive and negative symptoms (e.g. motivational and hedonic impairments). The clinical management of negative symptoms using antidepressant treatments may need to be reconsidered.