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## Quantitative Research

This entry describes the definition, history, theories, and applications of quantitative methods in social work research. Unlike qualitative research, quantitative research emphasizes precise, objective, and generalizable findings. Quantitative methods are based on numerous probability and statistical theories, with rigorous proofs and support from both simulated and empirical data. Regression analysis plays a paramountly important role in contemporary statistical methods, which include event history analysis, generalized linear modeling, hierarchical linear modeling, propensity score matching, and structural equation modeling. Quantitative methods can be employed in all stages of a scientific inquiry ranging from sample selection to final data analysis.

## Longitudinal Structural Equation Modeling in Lifespan Developmental Analyses

Longitudinal structural equation modeling (LSEM) is used to answer lifespan relevant questions such as (a) what is the effect of one variable on change in and other, (b) what is the average trajectory or growth rate of some psychological variable, and (c) what variability is there in average trajectories and what predicts this variability. The first of these questions is often answered by a LSEM called an autoregressive cross-lagged (ACL) model. The other two questions are most typically answered by an LSEM called a latent growth curve (LGC). These models can be applied to a few time waves (measured over several years) or to many time waves (such as present in diary studies) and can be altered, expanded, or even integrated. However, decisions on what model to use must be driven by the research question. The right tool for the job is not always the most complex. And, more importantly, the right tool must be matched to the best possible research design. Sometimes in lifespan research the right tool is LSEM. However, researchers should prioritize research design as well as careful specification of the processes and mechanisms they are interested in rather than simply choosing the most complicated LSEM they can find.

## Meta-Analytic Structural Equation Modeling

Meta-analysis and structural equation modeling (SEM) are two popular statistical models in the social, behavioral, and management sciences. Meta-analysis summarizes research findings to provide an estimate of the average effect and its heterogeneity. When there is moderate to high heterogeneity, moderators such as study characteristics may be used to explain the heterogeneity in the data. On the other hand, SEM includes several special cases, including the general linear model, path model, and confirmatory factor analytic model. SEM allows researchers to test hypothetical models with empirical data. Meta-analytic structural equation modeling (MASEM) is a statistical approach combining the advantages of both meta-analysis and SEM for fitting structural equation models on a pool of correlation matrices. There are usually two stages in the analyses. In the first stage of analysis, a pool of correlation matrices is combined to form an average correlation matrix. In the second stage of analysis, proposed structural equation models are tested against the average correlation matrix. MASEM enables researchers to synthesize researching findings using SEM as the research tool in primary studies. There are several popular approaches to conduct MASEM, including the univariate-r, generalized least squares, two-stage SEM (TSSEM), and one-stage MASEM (OSMASEM). MASEM helps to answer the following key research questions: (a) Are the correlation matrices homogeneous? (b) Do the proposed models fit the data? (c) Are there moderators that can be used to explain the heterogeneity of the correlation matrices? The MASEM framework has also been expanded to analyze large datasets or big data with or without the raw data.

## Cross-Cultural Measurement in Social Work Research and Evaluation

Cross-cultural measurement is an important topic in social work research and evaluation. Measuring health related concepts accurately is necessary for researchers and practitioners who work with culturally diverse populations. Social workers use measurements or instruments to assess health-related outcomes in order to identify risk and protective factors for vulnerable, disadvantaged populations. Culturally validated instruments are necessary, first, to identify the evidence of health disparities for vulnerable populations. Second, measurements are required to accurately capture health outcomes in order to evaluate the effectiveness of interventions for cross-cultural populations. Meaningful, appropriate, and practical research instruments, however, are not always readily available. They may have bias when used for populations from different racial and ethnic groups, tribal groups, immigration and refugee status, gender identities, religious affiliations, social class, and mental or physical abilities. Social work researchers must have culturally reliable and valid research instruments to accurately measure social constructs and ensure the validity of outcomes with cultural populations of interest. . In addition, culturally reliable and valid instruments are necessary for research which involves comparisons with different cultural groups. Instruments must capture the same conceptual understanding in outcomes across different cultural groups to create a basis for comparison. Cross-cultural instruments must also detect and ascertain the same magnitude in the changes in health outcomes, in order to accurately determine the impact of factors in the social environment as well as the influence of micro, mezzo, and macro-level interventions. This reference provides an overview of issues and techniques of cross-cultural measurement in social work research and evaluation. Applying systematic, methodological approaches to develop, collect, and assess cross-cultural measurements will lead to more reliable and valid data for cross-cultural groups.

## Structural Equation Modelling

Structural equation modelling (SEM) is a family of models where multivariate techniques are used to examine simultaneously complex relationships among variables. The goal of SEM is to evaluate the extent to which proposed relationships reflect the actual pattern of relationships present in the data. SEM users employ specialized software to develop a model, which then generates a model-implied covariance matrix. The model-implied covariance matrix is based on the user-defined theoretical model and represents the user’s beliefs about relationships among the variables. Guided by the user’s predefined constraints, SEM software employs a combination of factor analysis and regression to generate a set of parameters (often through maximum likelihood [ML] estimation) to create the model-implied covariance matrix, which represents the relationships between variables included in the model. Structural equation modelling capitalizes on the benefits of both factor analysis and path analytic techniques to address complex research questions. Structural equation modelling consists of six basic steps: model specification; identification; estimation; evaluation of model fit; model modification; and reporting of results. Conducting SEM analyses requires certain data considerations as data-related problems are often the reason for software failures. These considerations include sample size, data screening for multivariate normality, examining outliers and multicollinearity, and assessing missing data. Furthermore, three notable issues SEM users might encounter include common method variance, subjectivity and transparency, and alternative model testing. First, analyzing common method variance includes recognition of three types of variance: common variance (variance shared with the factor); specific variance (reliable variance not explained by common factors); and error variance (unreliable and inexplicable variation in the variable). Second, SEM still lacks clear guidelines for the modelling process which threatens replicability. Decisions are often subjective and based on the researcher’s preferences and knowledge of what is most appropriate for achieving the best overall model. Finally, reporting alternatives to the hypothesized model is another issue that SEM users should consider when analyzing structural equation models. When testing a hypothesized model, SEM users should consider alternative (nested) models derived from constraining or eliminating one or more paths in the hypothesized model. Alternative models offer several benefits; however, they should be driven and supported by existing theory. It is important for the researcher to clearly report and provide findings on the alternative model(s) tested. Common model-specific issues are often experienced by users of SEM. Heywood cases, nonidentification, and nonpositive definite matrices are among the most common issues. Heywood cases arise when negative variances or squared multiple correlations greater than 1.0 are found in the results. The researcher could resolve this by considering a small plausible value that could be used to constrain the residual. Non-positive definite matrices result from linear dependencies and/or correlations greater than 1.0. To address this, researchers can attempt to ensure all indicator variables are independent, inspect output manually for negative residual variances, evaluate if sample size is appropriate, or re-specify the proposed model. When used properly, structural equation modelling is a powerful tool that allows for the simultaneous testing of complex models.

## Dyadic Designs in Lifespan Developmental Methodology

The study of development across the lifespan has traditionally focused on the individual. However, dyadic designs within lifespan developmental methodology allow researchers to better understand individuals in a larger context that includes various familial relationships (husbands and wives, parents and children, and caregivers and patients). Dyadic designs involve data that are not independent, and thus outcome measures from dyad members need to be modeled as correlated. Typically, non-independent outcomes are appropriately modeled using multilevel or structural equation modeling approaches. Many dyadic researchers use the actor-partner interdependence model as a basic analysis framework, while new and exciting approaches are coming forth in the literature. Dyadic designs can be extended and applied in various ways, including with intensive longitudinal data (e.g., daily diaries), grid sequence analysis, repeated measures actor/partner interdependence models, and vector field diagrams. As researchers continue to use and expand upon dyadic designs, new methods for addressing dyadic research questions will be developed.