Análisis SEM, Ecuaciones estructurales modelos no lineales

Introduction to Structural Equation Models

Overview of the Course and Instructor

• The speaker, Basílica María Margalina, introduces herself as a professor at the University 1 de diciembre de 1918 in Albaulia, Romania, and manager of Ivas Group.

• She mentions that this session is part of a course on structural equation models and addresses the missed connection due to Ecuador's carnival holiday.

Previous Class Recap

• In the previous class, she covered how to evaluate measurement models for latent variables and analyze structural models.

• Key topics for this class include advanced analysis techniques: mediation analysis, moderation analysis, and non-linear relationships.

Advanced Analysis Techniques

Mediation and Moderation Analysis

• The instructor explains that understanding mediation (simple and multiple) and moderation (with continuous or categorical variables) is essential before delving into non-linear relationships.

Software License Information

• Students are informed about access to materials uploaded on the course platform, including a professional software license valid until April 19.

• Instructions are provided for downloading SmartP software compatible with various operating systems (Windows, Mac, Linux).

Using SmartP Software

Installation Steps

• After downloading SmartP software, students must copy a provided activation key to activate their licenses.

• The software interface can be switched to Spanish through preferences after installation.

Understanding Mediation vs. Moderation

Importance of Correlation in Causality

• The instructor emphasizes understanding the difference between mediation and moderation analyses as they are more advanced forms of regression analysis.

Correlation Does Not Imply Causation

• A critical point made is that correlation is necessary but not sufficient for establishing causality; statistical evidence alone cannot confirm causal relationships without theoretical backing.

The Role of Theory in Social Sciences

Statistical Analysis vs. Theory

• In social sciences research, theory holds greater importance than statistical analysis; statistics serve primarily to test hypotheses derived from theoretical frameworks.

Misleading Correlations

• Examples illustrate that high correlations can exist between unrelated variables (e.g., drowning accidents vs. Nicolas Cage movies), highlighting the need for careful interpretation of data.

Understanding Mediation in Structural Equation Modeling

Introduction to Mediation

• The discussion begins with the introduction of two variables, X and Y, emphasizing a multi-stage relationship rather than a simple cause-effect process.

• It is explained that in mediation analysis, an exogenous variable (independent variable) influences a mediator, which then affects the endogenous variable (dependent variable).

Example of Direct Relationship

• A direct relationship example is provided: increasing university requirements negatively impacts student pass rates. This illustrates a straightforward cause-effect scenario without mediation.

• When introducing a mediator, the complexity increases; now there are two hypotheses regarding how increased requirements affect study time and subsequently pass rates.

Hypotheses Development

• The first hypothesis suggests that higher requirements lead to more study time needed by students. The second posits that more study time increases the likelihood of passing.

• In mediation models, both direct and indirect relationships must be included for comprehensive analysis.

Formulating Mediation Hypotheses

• The mediation hypothesis states that the relationship between requirements and passing rates is mediated by study time.

• Researchers can specify whether this mediation has a positive or negative effect on the outcome.

Structuring Hypotheses

• It's common practice to separately formulate hypotheses for direct effects and mediating effects based on theoretical frameworks and empirical studies.

• The formulation depends heavily on existing theories and prior empirical evidence supporting these relationships.

Types of Effects in Mediation Models

• In mediation models, three types of effects are identified: direct effect (X to Y), indirect effect (through mediator), and total effect combining both pathways.

• Understanding these effects helps clarify how changes in one variable influence another through mediators.

Calculating Effects

• The indirect effect can be calculated by multiplying regression coefficients from X to M (mediator), then from M to Y (outcome).

• Total effect combines both direct and indirect paths, providing insight into overall impact within the model.

Analyzing Mediation Outcomes

• During analysis, it’s possible not to find any mediation or direct effects; this indicates potential flaws in theoretical assumptions requiring reevaluation.

Understanding Mediation Effects in Statistical Models

The Importance of Statistical Significance

• The direct effect is statistically significant, while the indirect effect is not. This raises the question of whether to include the mediating variable in the model or omit it, as non-significance can be a crucial finding.

• A special issue in the Journal of Marketing Analytics discusses the implications of statistical non-significance and its potential importance for scientific contributions. Valid results are often expected to show statistical significance for publication in high-impact journals.

Interpreting Results

• The interpretation of results is critical; sometimes, a lack of statistical significance can provide valuable insights into theoretical frameworks and practical applications. Understanding both significant and non-significant findings is essential for research advancement.

Types of Mediation

• Three types of mediation effects are identified:

• Complementary Mediation: Both direct and indirect effects are statistically significant with the same sign, indicating partial mediation.

• Competitive Mediation: Both effects are significant but have opposite signs, suggesting they compete against each other while still being partially mediated.

• Total Mediation: Only the indirect effect is statistically significant, indicating complete mediation without a direct effect present.

Evaluation Process in Software Analysis

• The analysis process begins with evaluating the measurement model based on whether it’s reflective or formative before moving on to structural model evaluation which includes assessing collinearity and both direct and indirect effects (P1 and P2). Power explanatory and predictive capabilities are also evaluated at this stage.

• Variance explained (an index calculated as indirect effect divided by total effect) provides additional insight into mediation but can only be applied to complementary mediation scenarios due to percentage constraints on competitive mediation outcomes. Interpretation thresholds include:

• Total mediation if >80%

• Partial mediation if between 20%–80%

• No mediation if <20%

Implications of Non-Significant Indirect Effects

• Even when an indirect effect shows significance, if its contribution to total variance explained is low (<20%), it may indicate that other unconsidered variables or moderating effects could explain why more substantial results were not achieved. Further investigation into these factors may be necessary for comprehensive understanding.

Practical Application Using Software

• An example will be demonstrated using software analysis focusing on corporate reputation models, specifically examining mediating effects among competition, likability, and loyalty metrics within a simple model framework from previous courses discussed earlier in this session. This practical application aims to solidify understanding through hands-on experience with data analysis tools used in research contexts.

Analysis of Statistical Models and Mediation Effects

Overview of Model Variables

• Discussion on the use of dependent variables in statistical models, emphasizing the increasing trend towards using a tail approach with sample sizes typically around 10,000.

• Initial calculations are performed using software (SmartPLS), highlighting the option to generate reports automatically or view analyses graphically.

Statistical Significance and Coefficients

• Importance of bootstrapping for assessing statistical significance, particularly focusing on HTMT criteria and confidence intervals.

• Identification of direct relationships between variables, noting a positive coefficient (0.50) and T-statistic (11), indicating significant statistical relevance when T > 1.96.

Direct Effects and Consumer Loyalty

• Analysis reveals a significant direct relationship where an increase in customer satisfaction by one standard deviation correlates with increased consumer loyalty.

• The model allows for adjustments in displayed statistics, including coefficients and P-values, enhancing interpretability.

Indirect Effects and Mediation Analysis

• Examination of specific indirect effects through mediation; QUSA mediates between competition (COP) and loyalty (QSL).

• Noted that while some indirect effects have low coefficients, they still hold statistical significance; variance explained is expected to be lower for these cases.

Total Effects Assessment

• Evaluation of total effects shows that most influence from competition on loyalty occurs indirectly through satisfaction rather than directly.

• Acknowledgment that the total effect coefficient indicates minimal direct significance but highlights substantial indirect pathways via satisfaction metrics.

Mediation Types: Simple vs. Multiple

• Clarification on different types of mediation; simple mediation involves one mediator while multiple mediation incorporates two or more mediators affecting the independent-dependent variable relationship.

• Results indicate partial mediation where both direct and indirect effects contribute significantly to explaining consumer loyalty influenced by sympathy factors.

This structured summary encapsulates key insights from the transcript regarding statistical modeling techniques, focusing on mediation analysis within consumer behavior studies.

Analysis of Indirect Effects and Mediation

Understanding Total Indirect Effects

• The analysis begins with examining individual mediating effects, comparing specific indirect effects (P1 multiplied by P2) against the direct effect (P3).

• It is essential to include all hypothesized relationships in the model without testing them separately for each mediation relationship.

Model Creation and Modification

• The speaker demonstrates how to create a new model in software, emphasizing that it should reflect both direct and indirect relationships.

• A simple model is duplicated to illustrate multiple mediation, highlighting the need for adjustments in connections between variables.

Statistical Significance and Coefficients

• The analysis focuses on evaluating specific indirect effects for statistical significance; if significant, it indicates a valid mediation effect.

• Observations reveal that while some coefficients show low statistical significance, the total indirect effect remains relevant.

Joint Mediation Effects

• The combined mediation effect of sympathy and satisfaction between competition and loyalty yields a positive coefficient of 0.43.

• This scenario exemplifies parallel mediation where both mediators contribute positively to the outcome.

Series Mediation Analysis

• When adding a series mediator hypothesis, calculations must consider interactions between mediators alongside direct effects.

• Adjustments in modeling are necessary when analyzing series mediation; maintaining clarity in variable connections is crucial.

Bootstrapping Results Interpretation

• Bootstrapping results indicate no change in direct significance despite additional hypotheses being tested.

• Specific indirect effects remain statistically significant across various models, reinforcing the presence of meaningful mediation.

Conclusion on Mediation Analysis

• The session wraps up with an invitation for questions regarding mediation analysis before transitioning into moderation analysis topics.

Analysis of Moderation and Mediation in Variables

Understanding the Difference Between Mediation and Moderation

• The analysis distinguishes between mediation and moderation, highlighting that while both involve a third variable, moderation directly influences the relationship between two correlated variables rather than acting as a vehicle for effect transfer.

• Mediation explains how variable X affects Y through another variable, whereas moderation clarifies under what conditions X impacts the dependent variable Y.

Characteristics of Moderator Variables

• The effect of X on Y can vary based on the level of the moderator variable, which can change both the intensity and direction (sign) of this relationship.

• Continuous moderator variables are measured on a metric scale (e.g., hours studied), allowing precise calculations of differences between values.

• Examples of continuous variables include income, age, units sold, and profitability; these metrics allow for distance calculations from an origin point.

Categorical Moderator Variables

• Categorical moderators can be binary (dummy variables coded as 0 or 1), such as gender. These are essential for analyzing relationships in different groups.

• Other categorical examples include service types; while binary categories are common, there can also be multi-category dummy variables.

Hypothesis Testing with Moderators

• An example hypothesis suggests that material quality in a course affects grades depending on study time; here, study time acts as a continuous moderator influencing outcomes.

• In contrast to continuous moderators, categorical moderators like gender may influence how material quality impacts grades across different student demographics.

Effects Analysis in Moderation

• The analysis compares groups based on whether they have included moderating effects; direct effects refer to relationships without considering moderators.

• When including moderating effects, the relationship between X and Y changes—this is termed either simple or conditioned effect.

Calculating Interaction Effects

• To determine direct effects accurately before introducing moderating factors is crucial since results differ significantly once moderators are included.

• The strength of relationships is assessed by examining how varying levels of the moderator affect outcomes when standardized data is used.

• Key terms include P1 (hypothesis indicator), P2 (conditional effect), and P3 (interaction term), which collectively represent moderation's impact on relationships between independent and dependent variables.

Mathematical Representation of Moderation Effects

• A mathematical expression illustrates how to calculate moderation effects by incorporating interaction terms into structural equation models for accurate measurement.

This structured overview captures key insights from the transcript regarding mediation versus moderation analysis within statistical modeling frameworks.

Understanding Moderation in Structural Equation Modeling

Interaction Terms and Measurement Models

• The discussion begins with the concept of interaction terms, specifically how to measure them through multiplication of latent variables (m1 with x3, m1 with x4, m2 with x3, and m2 with x4).

• It is noted that the calculation of an index for a variable differs based on whether the model is reflective or formative. This index is crucial for understanding moderation effects.

• The process involves determining latent variable scores first before using these scores as measures for the moderator variable in a two-step approach.

Example: Study Time and Switching Costs

• An example is provided where switching costs are hypothesized to moderate the relationship between customer satisfaction and loyalty.

• Literature suggests that higher switching costs weaken the effect of satisfaction on loyalty; customers may remain loyal despite dissatisfaction when switching costs are high.

Questionnaire Design

• Questions have been included in the questionnaire to measure switching costs, which are essential for analyzing their moderating effect on satisfaction and loyalty.

• The analysis aims to confirm that as switching costs increase, the relationship between satisfaction and loyalty becomes weaker.

Software Implementation

• Demonstration of how to include moderation effects in Smart PLS software by connecting indicators related to switching costs directly to customer satisfaction.

• Bootstrapping is initiated within Smart PLS to analyze structural coefficients and significance levels.

Results Interpretation

• A negative moderation coefficient was found, indicating statistical significance (p < 0.05), confirming that increased switching costs weaken the relationship between satisfaction (QUSA) and loyalty (QSL).

• Further analysis includes examining effect sizes (f²), which indicate a medium level of moderation effect based on established thresholds from literature.

Conclusion on Moderation Effects

• The f² value indicates a medium effect size for moderation; this suggests meaningful insights into how switching costs influence customer behavior.

• Analysis also includes visual representation of slopes showing different relationships under varying conditions of switching cost values.

Analysis of Change Costs and Their Impact on Loyalty

Understanding the Relationship Between Change Costs and Loyalty

• The discussion begins with an examination of how changes in the value of change costs affect loyalty, noting a positive slope in the relationship between these variables.

• A specific calculation is presented where, at lower levels of change costs, the slope is 0.467, indicating a significant effect on loyalty.

• At higher levels of change costs, the effect shifts to -0.071 due to a negative moderating effect, demonstrating that increased change costs can diminish loyalty.

Indirect Effects and Moderation

• The speaker introduces indirect conditional effects and mentions that mediation and moderation effects will be explained later in detail.

• It is noted that while continuous moderator variables have been discussed, categorical moderators (often binary) also play a role but come with unique challenges in analysis.

Challenges with Categorical Variables

• The use of binary variables for moderation analysis is highlighted; issues arise because they lack a meaningful zero reference point compared to continuous variables.

• Centering categorical variables around their mean helps interpret moderator effects better; however, binary categories complicate this process as they do not provide a clear zero point for comparison.

Conducting Moderation Analysis

• For effective moderation analysis using binary variables, it’s crucial to code them as 0 and 1 rather than other values like 1 and 2 to ensure accurate results.

• The speaker explains how to set up moderation analysis within software by connecting service type as a moderator variable for further calculations.

Statistical Significance and Findings

• After running analyses, it becomes evident that there is no statistical significance found regarding the moderating effect based on service type among mobile phone customers with contracts versus prepaid users.

• The F-squared statistic indicates very low significance (0.001), reinforcing previous findings about weak moderating effects related to service types in customer loyalty studies.

Direct Conditional Effects Comparison

• Differences are observed when comparing direct conditional effects based on service type values; however, variations are minimal (e.g., 0.53 vs. 0.48).

• Emphasis is placed on understanding that moderation analysis focuses specifically on how one variable's relationship strength varies with another variable's changes rather than comparing entire models across groups.

Analysis of Binary Variables and Moderation

Understanding Binary Variables in Group Analysis

• The comparison of the entire model and multigroup analysis is more common with binary variables, while moderation analysis is typically seen with continuous variables.

• When dealing with categorical variables that have multiple values, a multigroup analysis may be preferable; however, focusing on a specific relationship can still be valid.

Importance of Variable Coding

• Emphasizes the significance of variable coding in analyses. Results are documented in the manual for reference.

• Discusses simple and multiple mediation analysis, as well as moderation analysis involving both continuous and categorical variables.

Mediated Moderation Analysis

• Introduces moderated mediation where a moderator interacts with a mediator, affecting the indirect effect based on the moderator's value.

• Explains how this interaction leads to an indirect effect that can be termed either conditioned or simple.

Mathematical Representation of Effects

• The mathematical expression for conditioned effects is referred to as the "highes index," which quantifies how a moderator influences the indirect effect from X to Y through M.

Steps for Analyzing Moderated Mediation

• Outlines the process: start with evaluating the measurement model, then assess direct effects followed by conditioned or moderated effects.

• Highlights that interaction terms must connect both mediator and moderator to derive results from software tools effectively.

Modeling Techniques and Visualization

Drawing Variables in Models

• Discusses methods for visualizing models by selecting indicators and naming variables appropriately within software tools.

Conditional Mediation Example

• Provides an example where mediation between competition and loyalty is analyzed under conditions influenced by switching costs.

Managing Indicator Visibility

• Suggestion to hide indicators when working with complex models to enhance clarity during result interpretation.

Bootstrapping Results Interpretation

Evaluating Model Coefficients

• Mentions calculating bootstrapping results to observe changes in effects; highlights positive moderation without statistical significance (P-value = 0.31).

Direct Effect Assessment

• Indicates plans to calculate bootstrapping again for clearer insights into direct effects within structural models.

Analysis of Conditional Effects and Non-Linear Relationships

Comparison of Conditional Effects

• The Smart PLS tool allows for the comparison of reports, tables, graphs, and results. Notably, a coefficient change from 0.14 to 0 indicates a significant difference in conditional effects.

Understanding Moderation and Mediation

• While analyzing the extended model with moderation, it is essential to calculate OPS (observed power statistics) and analyze slopes to understand relationships better.

Evaluating Statistical Significance

• The LF square value is at the lower limit of effect size; without statistical significance, further analysis may not be warranted. The relationship between variables should be examined based on cost values.

Focus on Indirect Effects

• Emphasis is placed on understanding indirect conditional effects within moderated mediation frameworks. A specific indirect effect value of 0.029 is noted.

Exploring Non-Linear Relationships

• The discussion transitions to non-linear relationship analyses, highlighting that structural equation models (SEMs) are fundamentally based on linear regression models but often encounter non-linear relationships in real-world data.

Types of Non-Linear Relationships

Common Forms of Non-Linearity

• Research has identified common non-linear relationships such as U-shaped and inverted U-shaped curves in various fields like operations research and corporate financial performance.

Contextual Variability in Relationships

• Different contexts yield varying types of relationships; for instance, satisfaction versus loyalty can exhibit S-shaped patterns depending on specific conditions.

Modeling Non-Linearity in Structural Equations

Quadratic Functions in Analysis

• Quadratic functions represent one type of non-linearity where the dependent variable is squared. This leads to changes in sign when coefficients are analyzed within certain ranges.

Implementing Structural Equation Models

• To model quadratic relationships using SEM, researchers introduce squared terms as dependent variables while maintaining linearity concerning parameters like beta coefficients.

Moderation Effects in Structural Equation Modeling

Understanding Auto-moderation

• Auto-moderation occurs when an independent variable moderates its own relationship with a dependent variable; this requires careful modeling within SEM frameworks.

Best Practices for Estimation

• Utilizing standardized coefficients enhances clarity during analysis. Quadratic effects are frequently studied due to their prevalence across social sciences research contexts.

Two-Step Methodology for Structural Equation Models

Steps for Effective Analysis

• The two-step method involves calculating latent variable scores first before applying these scores to measure quadratic effects effectively within SEM frameworks.

Understanding Quadratic Effects in SmartPLS

Introduction to Quadratic Effects

• The discussion begins with the importance of measuring the effect of quadratic interactions, emphasizing the two-stage method's effectiveness for both reflective and formative models.

• A non-linear relationship is introduced, specifically focusing on quadratic effects represented mathematically as m = a^2 , which will be demonstrated using SmartPLS.

Advanced Analysis Techniques

• The advanced manual for PLSCS provides insights into corporate reputation analysis, highlighting how to install and utilize advanced methods for analyzing non-linear relationships.

• Demonstration of drawing models in SmartPLS is presented, showing how to incorporate quadratic effects by selecting specific model relationships.

Statistical Significance and Model Comparison

• The process of calculating statistical significance for quadratic effects is discussed, revealing a coefficient of -0.04 that approaches statistical significance under certain conditions.

• Emphasis on comparing models to determine if including a quadratic effect adds value; results show minimal increase in R-squared from 0.562 to 0.56, questioning the necessity of this inclusion.

Exploring Non-linear Effects

• It’s noted that while software like SmartPLS does not support S-shaped effect analyses directly, alternative methods are available through latent variable scores.

• Instructions are provided on exporting data from SmartPLS to Excel for further analysis, allowing users to manipulate latent variable scores effectively.

New Features in SmartPLS

• A new feature allows users to create databases containing latent scores directly within SmartPLS, enhancing data management capabilities.

• Recent updates enable users to perform operations such as addition or multiplication on indicators within the software, expanding analytical possibilities beyond traditional methods.

Exploring Variable Creation and Data Analysis in SmartPLS

Challenges with Variable Creation

• The speaker discusses difficulties in creating a variable, expressing uncertainty about whether it has been saved correctly.

• There is a need to understand how to combine latent variables, noting that their scores can vary and may even be negative based on results.

Data Exporting Issues

• The speaker attempts to export data but finds limitations, only able to save as comma-separated values (CSV), which complicates calculations.

• Acknowledges the challenge of handling missing data when trying to multiply latent variable scores for analysis.

Advanced Analytical Techniques

• Emphasizes the importance of multiplying quadratic effect scores with causal scores to derive third power metrics.

• Mentions the potential for errors due to database issues while using SmartPLS for analysis.

Structural Equation Modeling Insights

• Discusses various advanced topics within structural equation modeling (SEM), including predictive comparisons between models and confirmatory factor analysis.

• Highlights the significance of identifying unobserved heterogeneity through multigroup analysis, particularly regarding gender differences.

Hierarchical Component Models and Importance Performance Analysis

• Introduces hierarchical component models used for multidimensional variables like corporate reputation, combining dimensions into a single construct.

• Explains the combination of necessity condition analysis with importance-performance mapping in SmartPLS, assessing independent variables' roles in predicting dependent outcomes.

Upcoming Events and Resources

• Invites participation in an upcoming conference at the University of Mauritius, emphasizing opportunities for publication.

• Encourages following their company on social media for free statistical analysis courses covering various techniques beyond just PLS.

Course Conclusion and Resources

Encouragement to Continue Learning

• The speaker encourages participants to follow their YouTube channel for further learning on statistical techniques, emphasizing the importance of continuous education.

• Participants are invited to reach out via email (info@bitasur.com) if they have questions about the course material, specifically mentioning that they should identify themselves as educators from UPS in Ecuador.

Course Evaluation and Feedback

• A questionnaire will be shared on the course platform for participants to assess their understanding of the content covered during the course.

• The speaker acknowledges that the course duration was limited, making it challenging to cover extensive statistical measures effectively.

Final Thoughts and Personal Connection

• The speaker expresses gratitude for being part of the participants' learning journey and encourages them to practice what they've learned despite time constraints.

• A personal note is shared about living in Ecuador for seven years, highlighting fond memories and a connection with the local culture.