Posted By University of Wisconsin-Madison
The classic reference on this topic is Baron, R. M., & Kenny, D. A. (1986). The moderator-mediator variable distinction in social psychological research: Conceptual, strategic, and statistical considerations. Journal of Personality and Social Psychology, 51, 1173-1182.
Most of what is written here comes directly from this classic paper.
* Moderator variables - "In general terms, a moderator is a qualitative (e.g., sex, race, class) or quantitative (e.g., level of reward) variable that affects the direction and/or strength of the relation between an independent or predictor variable and a dependent or criterion variable. Specifically within a correlational analysis framework, a moderator is a third variable that affects the zero-order correlation between two other variables. ... In the more familiar analysis of variance (ANOVA) terms, a basic moderator effect can be represented as an interaction between a focal independent variable and a factor that specifies the appropriate conditions for its operation." p. 1174
* Mediator variables - "In general, a given variable may be said to function as a mediator to the extent that it accounts for the relation between the predictor and the criterion. Mediators explain how external physical events take on internal psychological significance. Whereas moderator variables specify when certain effects will hold, mediators speak to how or why such effects occur." p. 1176
The general test for mediation is to examine the relation between the predictor and the criterion variables, the relation between the predictor and the mediator variables, and the relation between the mediator and criterion variables. All of these correlations should be significant. The relation between predictor and criterion should be reduced (to zero in the case of total mediation) after controlling the relation between the mediator and criterion variables.
Another way to think about this issue is that a moderator variable is one that influences the strength of a relationship between two other variables, and a mediator variable is one that explains the relationship between the two other variables. As an example, let's consider the relation between social class (SES) and frequency of breast self-exams (BSE). Age might be a moderator variable, in that the relation between SES and BSE could be stronger for older women and less strong or nonexistent for younger women. Education might be a mediator variable in that it explains why there is a relation between SES and BSE. When you remove the effect of education, the relation between SES and BSE disappears.
Source: http://psych.wisc.edu/henriques/mediator.html
Saturday, August 28, 2010
Thursday, August 26, 2010
International Higher Education 2010 Conference in Perth, Australia
IADIS International Conference on International Higher Education 2010
29, 30 November and 1 December 2010 – Perth, Australia
Call for Papers
Technology like transport, communication and media-based learning have increased our ambitions to make education more global and international. Higher education has gradually felt more affinity towards the exchange of students; Diversity and learning in concentration with different cultures that has settled as road map for the coming decades. Firstly, motivation for international higher education to promote students’ mindset towards different cultures, languages and traditions. Secondly, allowing students to learn multi-cultural contexts to anticipate to the later career that involve cooperation in international teams. As inevitable side effect, universities welcome international students as source of income and exchange knowledge and skills. To be more precisely, students will take part of their courses abroad, and at least they should match a similar amount of incoming students in order to play par.
This conference aims at the scientific, pragmatic and policy awareness among scholars who face the direct need to make their curricula more culturally fair. European exchange programs like the Erasmus Mundus, the U.S. Council on International Educational Student Exchange, and the Euro-American “Atlantis” program, they all envisage an urgent agenda on how to balance local with the more global criteria in higher education. This conference helps you to build your networks and international consortia on how to be a key player in this emergent trend.
Though not exclusive, the next topics are welcome for papers, posters, symposia and forums
1. Technologies for spreading learning around the world
2. Higher Education and International student exchange
3. Learning far away from home and close to your future colleagues
4. Learning in multicultural contexts
5. Virtual presence as option for extending the students’ learning space
6. Formal and pragmatic obstacles and opportunities in student exchange programs
7. Double- versus joint degrees
8. Funding resources for staff and student exchange
9. How to establish campuses as multicultural communities
10. Coping with incompatibility in semester-, trimester and quarter year course periods
11. Trade-offs between student exchange in the bachelor- versus the master stage?
12. Will English be the default language for master courses around the globe?
13. Does studying abroad imply “living together with local students”, or prefer “international student houses”?
14. How to recruit highly talented students abroad?
15. How to defend the yielded higher criterion to the access of regional- and local students?
16. How to evaluate students’ readiness for studying abroad?
17. Acculturation: what preliminary intercultural need to be trained before been sent to a study abroad?
This conference will focus both on the acute main streams of student exchange:
- Eastern Asia to Europe, the U.S., Australia and New Zealand
- Among Western and Eastern European countries
- Among Spain, Portugal and Southern American countries
- Among Europe and the U.S.
The Conference will be composed of several types of contributions:
* Full Papers – These include mainly accomplished research results and have 8 pages at the maximum (5,000 words).
* Short Papers – These are mostly composed of work in progress reports or fresh developments and have 4 pages at maximum (2,500 words).
* Reflection Papers – These might review recent research literature pertaining to a particular problem or approach, indicate what the findings suggest, and/or provide a suggestion - with rationale and justification - for a different approach or perspective on that problem. Reflection papers might also analyze general trends or discuss important issues in topics related to Applied Computing. These have two pages at maximum (1500 words).
* Posters / Demonstrations – These have one page at the maximum (625 words) besides the poster itself (or demonstration) that will be exposed at the conference.
* Tutorials – Tutorials can be proposed by scholars or company representatives. A proposal of maximum 250 words is expected.
* Panels – Discussions on selected topics will be held. A proposal of maximum 250 words is expected.
* Invited Talks – These will be made of contributions from well-known scholars and company representatives. An abstract will be included in the conference proceedings.
* Doctoral Consortium - The Doctoral Consortium will discuss on going work of PhD students in an informal and formative atmosphere. Contributions to the consortium should take the form of either:
- a critical literature review of the research topic providing the rationale for the relevance and interest of the research topic; or
- a short paper discussing the research question(s), research objectives, research methodology and work done so far.
Doctoral Consortium Contributions should have a maximum 2,500 words (4 pages).
* Corporate Showcases & Exhibitions – The former enables Companies to present recent developments and applications, inform a large and qualified audience of your future directions and showcase company’s noteworthy products and services. There will be a time slot for companies to make their presentation in a room. The latter enables companies the opportunity to display its latest offerings of hardware, software, tools, services and books, through an exhibit booth. For further details please contact the publicity chair - secretariat@ihe-conf.org.
This is a blind peer-reviewed conference.
Important Dates:
- Submission Deadline (2nd call): 6 September 2010
- Notification to Authors (2nd call): 6 October 2010
- Final Camera-Ready Submission and Early Registration (1st call): Until 28 July 2010
- Late Registration (1st call): After 28 July 2010
- Conference: Perth, Australia, 29, 30 November and 1 December 2010
For more details: http://www.ihe-conf.org/
Sunday, August 22, 2010
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3rd International Conference on Teaching and Learning
About ICTL 2011:
INTI International University is organising a biennial International Conference on Teaching and Learning (ICTL 2011). This 3-day conference aims to provide a forum for educators, researchers, technologists and students to share their knowledge and expertise in teaching and learning; to stimulate high quality research work in teaching and learning so as to develop state-of-the-art educational technologies; and to promote intellectual discourse among the conference participants from the United Kingdom, United States, Canada, Australia, New Zealand, Europe and Asia. Over 350 participants from overseas and local universities or higher education institutions are expected to attend the conference.
Conference Theme:
Towards 21st Century Education: Student – Student Collaboration
Conference Venue and Date:
November 14 - 16, 2011
PARKROYAL Penang Hotel
Penang, Malaysia
All researchers, educators and technologists around the world are invited to contribute papers in this conference. Papers, not published elsewhere, are invited in the following topics:
* Instructional Strategy
* Instructional Technology
* E-Learning
* Assessment and Evaluation
* Classroom Management
For details on conference topic: http://ictl.intimal.edu.my/html_topics.php
Important Dates:
Call for papers: June 1, 2010
Proposal Due: April 29, 2011
Authors Notified: May 31, 2011
Early Registration Deadline: August 31, 2011
Proceeding Files Deadline: August 15, 2011
For further details: http://ictl.intimal.edu.my/index.php
2nd INTERNATIONAL CONFERENCE on BUSINESS and ECONOMIC RESEARCH- ICBER
2nd INTERNATIONAL CONFERENCE on BUSINESS and ECONOMIC RESEARCH- ICBER
DATE: 14-15 March 2011
VENUE: Holiday Villa Beach Resort and Spa, Langkawi Kedah, Malaysia
ISBN PROCEEDING: 978-967-5705-01-4
Important Dates:
SUBMIT PAPER TO: icber@internationalconference.com.my
ABSTRACT SUBMISSION DEADLINE: 16 Feb 2011
NOTIFICATION OF ABSTRACT ACCEPTANCE: 30 Feb 2011
FULL PAPER SUBMISSION DEADLINE: 20 Feb 2011
FINAL PAPER DUE: 10 Feb 2011
Theoerical and empirical papers in all areas of Accounting, Banking, Ecomonics, Finance, Management and Marketing are invited for the above International Conference. Please refer to the Major Field of Research. All papers will undergo double blind peer review process and all accepted papers will be published in the Refereed Conference Proceedings with an ISBN. "Best Paper Winners" will be selected from a block papers in each track and winners will receive a cerificate and their papers will be considered to be published in the "Journal of International Conference on Business and Economics Research" subject to compliance to their guidelines and conditions.
SESSION CHAIR
Participants may serve as the Session Chair. If you are interested, please indicate your willingness in the Registration Form. A certificate will be issued to all Chairs acknowledging their role at the conference.
For details: http://www.internationalconference.com.my/icber/icber.htm
DATE: 14-15 March 2011
VENUE: Holiday Villa Beach Resort and Spa, Langkawi Kedah, Malaysia
ISBN PROCEEDING: 978-967-5705-01-4
Important Dates:
SUBMIT PAPER TO: icber@internationalconference.com.my
ABSTRACT SUBMISSION DEADLINE: 16 Feb 2011
NOTIFICATION OF ABSTRACT ACCEPTANCE: 30 Feb 2011
FULL PAPER SUBMISSION DEADLINE: 20 Feb 2011
FINAL PAPER DUE: 10 Feb 2011
Theoerical and empirical papers in all areas of Accounting, Banking, Ecomonics, Finance, Management and Marketing are invited for the above International Conference. Please refer to the Major Field of Research. All papers will undergo double blind peer review process and all accepted papers will be published in the Refereed Conference Proceedings with an ISBN. "Best Paper Winners" will be selected from a block papers in each track and winners will receive a cerificate and their papers will be considered to be published in the "Journal of International Conference on Business and Economics Research" subject to compliance to their guidelines and conditions.
SESSION CHAIR
Participants may serve as the Session Chair. If you are interested, please indicate your willingness in the Registration Form. A certificate will be issued to all Chairs acknowledging their role at the conference.
For details: http://www.internationalconference.com.my/icber/icber.htm
Basic AMOS
AMOS is statistical software and it stands for analysis of a moment structures. AMOS is an added SPSS module, and is specially used for Structural Equation Modeling, path analysis, and confirmatory factor analysis. It is also known as analysis of covariance or causal modeling software. AMOS is a visual program for structural equation modeling (SEM). In AMOS, we can draw models graphically using simple drawing tools. AMOS quickly performs the computations for SEM and displays the results.
In calculation of SEM coefficients, AMOS uses the following methods:
* Maximum likelihood
* Unweighted least squares
* Generalized least squares
* Browne’s asymptotically distribution-free criterion
* Scale-free least squares
Construction of model in AMOS:
First, we have to run AMOS. By clicking the “start” menu and selecting the “AMOS graphic” option from AMOS, we can run AMOS. The moment AMOS starts running, a window appears called the “AMOS graphic.” In this window, we can manually draw our SEM model.
Attaching data in AMOS: By selecting a file name from the data file option, we can attach data in AMOS for SEM analysis. This option also appears if we will click on the “select data” icon.
Observed variable: In AMOS, a rectangle icon is used to draw the observed variable.
Unobserved variable: In AMOS, a circle icon is used to draw the unobserved variable.
Cause effect relationdship: A single headed arrow in AMOS is used to draw the cause effect relationship between the observed and unobserved variables.
Covariance: A double headed arrow is used in AMOS to draw the covariance between variables.
Error term: In AMOS, the error term icon is next to the unobserved variable icon, and it is used to draw the latent variable.
Naming the Variable: When we right click on a variable in a graphical window, the first option, “object properties,” is used to give the name of the varible in AMOS.
There are other icons as well, and these icons help in drawing the SEM model graphically. Icons such as erase icon, moving icon, caculate icon, view text, analysis properties, etc., help in drawing the SEM model graphically.
Understanding the text output in AMOS: After running the analysis, we can see the results on the graphic window. We can also see the text output. The graphic window will only show the standardized and unstandrized regressions and error term weights. All results will be shown in the text output.
AMOS will produce the following important output:
Variable Summary: In AMOS and its text output variable summery, we can see how many variables and which variables are used for SEM analysis. We can see how many observerd variables and how many unobserved variables were in the model.
Accessing the normality: In SEM model, data should be normaly distributed. AMOS will give the text output, and Skewness, Kurtosis and Mahalanobis d-squared test will tell us about the normality of the data.
Estimates: In AMOS text output, the estimate option will give the result for regression weight, standardized loading for factor, residual, correlation, covariance, direct effect, indirect effect, total effect, etc.
Modification index: In AMOS text output, the modification index result shows the reliability of the path drawn in the SEM model. If MI index value is large, then we can add more paths to the SEM model.
Model fit: In AMOS text output, Model fit option will give the result for goodness of fit model statistics. It will show all the goodness of fit indexes, such as GFI, RMR, TLI, BIC, RMSER, etc.
Error message: If there is any problem, during the process of drawing the model (for example, if we forget to draw the error term or if we draw the covariance between two variables, or if missing data is present), then AMOS will either not calculate the result or it will give an error message.
Source: http://www.statisticssolutions.com/statistics-software/amos/
Structural equation modeling
Structural equation modeling is a multivariate statistical analysis technique that is used to analyze structural relationships. Structural equation modeling technique is the combination of factor analysis and multiple regression analysis, and it is used to analyze the structural relationship between measured variables and latent constructs. Structural equation modeling is preferred by the researcher because it estimates the multiple and interrelated dependence in a single analysis.
In structural equation modeling, two types of variables are used endogenous variables and exogenous variables. In structural equation modeling, endogenous variables are equivalent to dependent variables. In structural equation modeling, exogenous variables are equal to the independent variable.
Structural equation modeling and theory:
In structural equation modeling, theory can be thought of as a set of relationships providing consistency and comprehensive explanations of the actual phenomena. Structural equation modeling consists of two types of models:
1. Measurement model: In structural equation modeling, the measurement model represents the theory that specifies how measured variables come together to represent the theory.
2. Structural model: In structural equation modeling, the structural model represents the theory that shows how constructs are related to other constructs.
Structural equation modeling is also called casual modeling because structural equation modeling tests the proposed casual relationships. The following assumptions are assumed in structural equation modeling:
1. Multivariate normal distribution: In structural equation modeling, the maximum likelihood method is used and assumed for multivariate normal distribution. Small changes in multivariate normality can lead to a large difference in the chi-square test.
2. Linearity: In structural equation modeling, a linear relationship is assumed between endogenous and exogenous variables.
3. Outlier: In structural equation modeling, data should be free of outliers. Outliers affect the model significance.
4. Sequence: In structural equation modeling, there should be a cause and effect relationship between endogenous and exogenous variables, and a cause has to occur before the event.
5. Non-spurious relationship: In structural equation modeling, observed covariance must be true.
6. Model identification: In structural equation modeling, equations must be greater than the estimated parameters or models should be over identified or exact identified. Under identified models are not considered in structural equation modeling.
7. Sample size: In structural equation modeling, most of the researchers prefer a 200 to 400 sample size with 10 to 15 indicators. As a rule of thumb, that is 10 to 20 times as many cases as variables.
8. Uncorrelated error terms: In structural equation modeling, error terms are assumed uncorrelated with other variable error terms.
9. Data: Interval data is used in structural equation modeling.
The following steps are involved in structural equation modeling:
1. Defining individual constructs: The first step in structural equation modeling is to define the constructs theoretically. Conduct a pretest to evaluate the item. A confirmatory test of the measurement model is conducted using CFA.
2. Developing the overall measurement model: In structural equation modeling, the measurement model is also known as path analysis. Path analysis is a set of relationships between exogenous and endogens variables. This is shown by the use of an arrow. The measurement model follows the assumption of unidimensionality. Measurement theory is based on the idea that latent constructs cause the measured variable and that the error term is uncorrelated within measured variables. In a measurement model, an arrow is drawn from the measured variable to the constructs.
3. Design the study to produce the empirical results: In this step of structural equation modeling, the researcher must specify the model. The researcher should design the study to minimize the likelihood of an identification problem. In structural equation modeling, order condition and rank condition methods are used to minimize the identification problem.
4. Assessing the measurement model validity: In structural equation modeling, assessing the measurement model is also called CFA. In CFA, a researcher compares the theoretical measurement against the reality model. In structural equation modeling, the result of the CFA must be associated with the constructs’ validity.
5. Specifying the structural model: In this step of structural equation modeling, structural paths are drawn between constructs. In the structural model, no arrow can enter an exogenous construct. A single-headed arrow is used to represent a hypothesized structural relationship between one construct and another. This shows the cause and effect relationship. In structural equation modeling, each hypothesized relationship uses one degree of freedom. In structural equation modeling, the model can be recursive or nonrecursive.
6. Examine the structural model validity: In the last step of structural equation modeling, a researcher examines the structural model validity. In structural equation modeling, a model is considered a good fit if the value of the chi-square test is insignificant, and at least one incremental fit index (like CFI, GFI, TLI, AGFI, etc.) and one badness of fit index (like RMR, RMSEA, SRMR, etc.) meet the predetermined criteria.
Source: http://www.statisticssolutions.com/methods-chapter/statistical-tests/structural-equation-modeling/
Path Analysis
In statistics analysis, path analysis is considered an extension of the regression model. In a path analysis model from the correlation matrix, two or more casual models are compared. In path analysis, the path of the model is shown by a circle and an arrow, which shows the causation. In path analysis, regression weight is predicated by the model, and is compared by the observed correlation matrix. Then the goodness of fit statistic is calculated in order to see the fitting of the model.
Key concepts and terms in path analysis:
Estimation method in Path analysis: In path analysis, simple OLS and maximum likelihood methods are used to predict the path.
Path model: In path analysis, a path model is a diagram which shows the independent, intermediate, and dependent variable. In path analysis, a single headed arrow shows the cause for the independent, intermediate and dependent variable. A double headed arrow shows the covariance between the two variables.
Exogenous and endogenous variables in path analysis: In path analysis, exogenous variables in a path model are those where no error points towards them, except the measurement error term. If exogenous variables are correlated to each other, then a double headed arrow will connect those variables. Endogenous variables may have both the incoming and outgoing arrows.
Path coefficient: In path analysis, a path coefficient is a standardized regression coefficient (beta), showing the direct effect of an independent variable on a dependent variable in the path model.
Disturbance terms: The residual error terms are also called disturbance terms in path analysis. Disturbance terms reflect the unexplained variance and measurement error.
Direct and indirect effect in path analysis: In path analysis, the path model has two types of effects. The first is the direct effect, and the second is the indirect effect. When the exogenous variable has an arrow directed towards the dependent variable, then it is said to be the direct effect. When an exogenous variable has an effect on the dependent variable, through the other exogenous variable, then it is said to be an indirect effect. To see the total effect of the exogenous variable, we have to add the direct and indirect effect. In path analysis, one variable may not have a direct effect, but it may have an indirect effect.
Significance and goodness of fit in path analysis: OLS and maximum likelihood methods are used to predict the path coefficient in path analysis. These days, statistical software like AMOS, SAS and LISREL, etc. are software that calculates the path coefficient and goodness of fit statistics automatically.
The following statistics are used to test the significance and goodness of fit of path analysis:
Chi-square statistics: Non-significant chi-square value in path analysis shows the goodness of fit model. Sometimes, chi-square statistics is significant. However, we still have to test one absolute fit index and one incremental fit index.
Absolute fit index: RMSEA: An absolute fit index using 90% confidence interval for RMSEA should be less than 0.08 for a goodness of fit model.
Increment fit index: CFI, GFI, NNFI, TLI, RFI and AGFI, etc. are some incremental fit indexes, which should be greater than 0.90 for a goodness of fit model.
Modification indexes: Modification indexes (MI) may be used to add arrows to the model. The larger the MI, the more arrows will be added to the model, which will improve the model fit.
Assumptions in Path analysis:
Linearity: In path analysis, relationships should be linear.
Interval level data: In path analysis, data should be at interval scale.
Uncorrelated residual term: In path analysis, error term should not be correlated to any variable.
Disturbance terms: In path analysis, disturbance terms should not be correlated to endogenous variables.
Multicollinearity: In path analysis, low multicollinearity is assumed. Perfect multicollinearity may cause problems in the path analysis.
Identification: In path analysis, the path model should not be under identified. Exactly identified or over identified models are good for path analysis.
Adequate sample size: Kline (1998) recommends that the sample size should be 10 times (or ideally 20 times) as many cases as parameters.
Source: http://www.statisticssolutions.com/methods-chapter/statistical-tests/path-analysis/
Confirmatory factor analysis
Confirmatory factor analysis (CFA) is a multivariate statistical procedure that is used to test how well the measured variables represent the number of constructs. Confirmatory factor analysis (CFA) and exploratory factor analysis (EFA) are similar techniques, but in exploratory factor analysis (EFA), data is simply explored and provides information about the numbers of factors required to represent the data. In exploratory factor analysis, all measured variables are related to every latent variable. But in confirmatory factor analysis (CFA), researchers can specify the number of factors required in the data and which measured variable is related to which latent variable. Confirmatory factor analysis (CFA) is a tool that is used to confirm or reject the measurement theory.
Terms and concepts in confirmatory factor analysis (CFA):
Theory: In confirmatory factor analysis (CFA), theory is a systematic set of causal relationships that provide the comprehensive explanation of a phenomenon.
Model: In confirmatory factor analysis (CFA), model is a specified set of dependant relationships that can be used to test the theory.
Path analysis: In confirmatory factor analysis (CFA), path analysis is used to test structural equations.
Path diagram: In confirmatory factor analysis (CFA), the path diagram shows the graphical representation of cause and effect relationships of the theory.
Endogenous variable: In confirmatory factor analysis (CFA), endogenous variables are the resulting variables that are a causal relationship.
Exogenous variable: In confirmatory factor analysis (CFA), exogenous variables are the predictor variables.
Confirmatory analysis: In confirmatory factor analysis (CFA), confirmatory analysis is used to test the pre-specified relationship.
Cronbach’s alpha: In confirmatory factor analysis (CFA), Cronbach’s alpha is used to measure the reliability of two or more construct indicators.
Identification: In confirmatory factor analysis (CFA), identification is used to test whether or not there are a sufficient number of equations to solve the unknown coefficient. In confirmatory factor analysis (CFA) identifications are of three types: (1) underidentified, (2) exact identified, and (3) over-identified.
Goodness of fit: In confirmatory factor analysis (CFA), goodness of fit is the degree to which the observed input matrix is predicted by the estimated model.
The following are the procedures involved in confirmatory factor analysis (CFA):
1. Defining individual construct: In confirmatory factor analysis (CFA), first we have to define the individual constructs. In confirmatory factor analysis (CFA), the first step involves the procedure that defines constructs theoretically. This involves a pretest to evaluate the construct items, and a confirmatory test of the measurement model that is conducted using confirmatory factor analysis (CFA), etc.
2. Developing the overall measurement model theory: In confirmatory factor
analysis (CFA), we should consider the concept of unidimensionality between construct error variance and within construct error variance. At least four constructs and three items per constructs should be present in the research.
3. Designing a study to produce the empirical results: In confirmatory factor analysis (CFA), the measurement model must be specified. In confirmatory factor analysis (CFA), most commonly, the value of one loading estimate should be one per construct. In confirmatory factor analysis (CFA), two methods are available for identification. The first is rank condition, and the second is order condition.
4. Assessing the measurement model validity: In confirmatory factor analysis (CFA), assessing the measurement model validity occurs when the theoretical measurement model is compared with the reality model to see how well the data fits. In confirmatory factor analysis (CFA), to check the measurement model validity, the number of the indicator helps us. For example, in confirmatory factor analysis (CFA), the factor loading latent variable should be greater than 0.7. Chi-square test and other goodness of fit statistics like RMR, GFI, NFI, RMSEA, SIC, BIC, etc., are some key indicators that help in measuring the model validity in confirmatory factor analysis (CFA).
Confirmatory factor analysis (CFA) and statistical software: Usually, statistical software like AMOS, LISREL, EQS and SAS are used for confirmatory factor analysis (CFA). In AMOS, visual paths are manually drawn on the graphic window and analysis is performed. In confirmatory factor analysis (CFA) in LISREL, confirmatory factor analysis (CFA) can be performed graphically as well as from the menu. In SAS, confirmatory factor analysis (CFA) can be performed by using the programming languages.
Source: http://www.statisticssolutions.com/methods-chapter/statistical-tests/confirmatory-factor-analysis/
In calculation of SEM coefficients, AMOS uses the following methods:
* Maximum likelihood
* Unweighted least squares
* Generalized least squares
* Browne’s asymptotically distribution-free criterion
* Scale-free least squares
Construction of model in AMOS:
First, we have to run AMOS. By clicking the “start” menu and selecting the “AMOS graphic” option from AMOS, we can run AMOS. The moment AMOS starts running, a window appears called the “AMOS graphic.” In this window, we can manually draw our SEM model.
Attaching data in AMOS: By selecting a file name from the data file option, we can attach data in AMOS for SEM analysis. This option also appears if we will click on the “select data” icon.
Observed variable: In AMOS, a rectangle icon is used to draw the observed variable.
Unobserved variable: In AMOS, a circle icon is used to draw the unobserved variable.
Cause effect relationdship: A single headed arrow in AMOS is used to draw the cause effect relationship between the observed and unobserved variables.
Covariance: A double headed arrow is used in AMOS to draw the covariance between variables.
Error term: In AMOS, the error term icon is next to the unobserved variable icon, and it is used to draw the latent variable.
Naming the Variable: When we right click on a variable in a graphical window, the first option, “object properties,” is used to give the name of the varible in AMOS.
There are other icons as well, and these icons help in drawing the SEM model graphically. Icons such as erase icon, moving icon, caculate icon, view text, analysis properties, etc., help in drawing the SEM model graphically.
Understanding the text output in AMOS: After running the analysis, we can see the results on the graphic window. We can also see the text output. The graphic window will only show the standardized and unstandrized regressions and error term weights. All results will be shown in the text output.
AMOS will produce the following important output:
Variable Summary: In AMOS and its text output variable summery, we can see how many variables and which variables are used for SEM analysis. We can see how many observerd variables and how many unobserved variables were in the model.
Accessing the normality: In SEM model, data should be normaly distributed. AMOS will give the text output, and Skewness, Kurtosis and Mahalanobis d-squared test will tell us about the normality of the data.
Estimates: In AMOS text output, the estimate option will give the result for regression weight, standardized loading for factor, residual, correlation, covariance, direct effect, indirect effect, total effect, etc.
Modification index: In AMOS text output, the modification index result shows the reliability of the path drawn in the SEM model. If MI index value is large, then we can add more paths to the SEM model.
Model fit: In AMOS text output, Model fit option will give the result for goodness of fit model statistics. It will show all the goodness of fit indexes, such as GFI, RMR, TLI, BIC, RMSER, etc.
Error message: If there is any problem, during the process of drawing the model (for example, if we forget to draw the error term or if we draw the covariance between two variables, or if missing data is present), then AMOS will either not calculate the result or it will give an error message.
Source: http://www.statisticssolutions.com/statistics-software/amos/
Structural equation modeling
Structural equation modeling is a multivariate statistical analysis technique that is used to analyze structural relationships. Structural equation modeling technique is the combination of factor analysis and multiple regression analysis, and it is used to analyze the structural relationship between measured variables and latent constructs. Structural equation modeling is preferred by the researcher because it estimates the multiple and interrelated dependence in a single analysis.
In structural equation modeling, two types of variables are used endogenous variables and exogenous variables. In structural equation modeling, endogenous variables are equivalent to dependent variables. In structural equation modeling, exogenous variables are equal to the independent variable.
Structural equation modeling and theory:
In structural equation modeling, theory can be thought of as a set of relationships providing consistency and comprehensive explanations of the actual phenomena. Structural equation modeling consists of two types of models:
1. Measurement model: In structural equation modeling, the measurement model represents the theory that specifies how measured variables come together to represent the theory.
2. Structural model: In structural equation modeling, the structural model represents the theory that shows how constructs are related to other constructs.
Structural equation modeling is also called casual modeling because structural equation modeling tests the proposed casual relationships. The following assumptions are assumed in structural equation modeling:
1. Multivariate normal distribution: In structural equation modeling, the maximum likelihood method is used and assumed for multivariate normal distribution. Small changes in multivariate normality can lead to a large difference in the chi-square test.
2. Linearity: In structural equation modeling, a linear relationship is assumed between endogenous and exogenous variables.
3. Outlier: In structural equation modeling, data should be free of outliers. Outliers affect the model significance.
4. Sequence: In structural equation modeling, there should be a cause and effect relationship between endogenous and exogenous variables, and a cause has to occur before the event.
5. Non-spurious relationship: In structural equation modeling, observed covariance must be true.
6. Model identification: In structural equation modeling, equations must be greater than the estimated parameters or models should be over identified or exact identified. Under identified models are not considered in structural equation modeling.
7. Sample size: In structural equation modeling, most of the researchers prefer a 200 to 400 sample size with 10 to 15 indicators. As a rule of thumb, that is 10 to 20 times as many cases as variables.
8. Uncorrelated error terms: In structural equation modeling, error terms are assumed uncorrelated with other variable error terms.
9. Data: Interval data is used in structural equation modeling.
The following steps are involved in structural equation modeling:
1. Defining individual constructs: The first step in structural equation modeling is to define the constructs theoretically. Conduct a pretest to evaluate the item. A confirmatory test of the measurement model is conducted using CFA.
2. Developing the overall measurement model: In structural equation modeling, the measurement model is also known as path analysis. Path analysis is a set of relationships between exogenous and endogens variables. This is shown by the use of an arrow. The measurement model follows the assumption of unidimensionality. Measurement theory is based on the idea that latent constructs cause the measured variable and that the error term is uncorrelated within measured variables. In a measurement model, an arrow is drawn from the measured variable to the constructs.
3. Design the study to produce the empirical results: In this step of structural equation modeling, the researcher must specify the model. The researcher should design the study to minimize the likelihood of an identification problem. In structural equation modeling, order condition and rank condition methods are used to minimize the identification problem.
4. Assessing the measurement model validity: In structural equation modeling, assessing the measurement model is also called CFA. In CFA, a researcher compares the theoretical measurement against the reality model. In structural equation modeling, the result of the CFA must be associated with the constructs’ validity.
5. Specifying the structural model: In this step of structural equation modeling, structural paths are drawn between constructs. In the structural model, no arrow can enter an exogenous construct. A single-headed arrow is used to represent a hypothesized structural relationship between one construct and another. This shows the cause and effect relationship. In structural equation modeling, each hypothesized relationship uses one degree of freedom. In structural equation modeling, the model can be recursive or nonrecursive.
6. Examine the structural model validity: In the last step of structural equation modeling, a researcher examines the structural model validity. In structural equation modeling, a model is considered a good fit if the value of the chi-square test is insignificant, and at least one incremental fit index (like CFI, GFI, TLI, AGFI, etc.) and one badness of fit index (like RMR, RMSEA, SRMR, etc.) meet the predetermined criteria.
Source: http://www.statisticssolutions.com/methods-chapter/statistical-tests/structural-equation-modeling/
Path Analysis
In statistics analysis, path analysis is considered an extension of the regression model. In a path analysis model from the correlation matrix, two or more casual models are compared. In path analysis, the path of the model is shown by a circle and an arrow, which shows the causation. In path analysis, regression weight is predicated by the model, and is compared by the observed correlation matrix. Then the goodness of fit statistic is calculated in order to see the fitting of the model.
Key concepts and terms in path analysis:
Estimation method in Path analysis: In path analysis, simple OLS and maximum likelihood methods are used to predict the path.
Path model: In path analysis, a path model is a diagram which shows the independent, intermediate, and dependent variable. In path analysis, a single headed arrow shows the cause for the independent, intermediate and dependent variable. A double headed arrow shows the covariance between the two variables.
Exogenous and endogenous variables in path analysis: In path analysis, exogenous variables in a path model are those where no error points towards them, except the measurement error term. If exogenous variables are correlated to each other, then a double headed arrow will connect those variables. Endogenous variables may have both the incoming and outgoing arrows.
Path coefficient: In path analysis, a path coefficient is a standardized regression coefficient (beta), showing the direct effect of an independent variable on a dependent variable in the path model.
Disturbance terms: The residual error terms are also called disturbance terms in path analysis. Disturbance terms reflect the unexplained variance and measurement error.
Direct and indirect effect in path analysis: In path analysis, the path model has two types of effects. The first is the direct effect, and the second is the indirect effect. When the exogenous variable has an arrow directed towards the dependent variable, then it is said to be the direct effect. When an exogenous variable has an effect on the dependent variable, through the other exogenous variable, then it is said to be an indirect effect. To see the total effect of the exogenous variable, we have to add the direct and indirect effect. In path analysis, one variable may not have a direct effect, but it may have an indirect effect.
Significance and goodness of fit in path analysis: OLS and maximum likelihood methods are used to predict the path coefficient in path analysis. These days, statistical software like AMOS, SAS and LISREL, etc. are software that calculates the path coefficient and goodness of fit statistics automatically.
The following statistics are used to test the significance and goodness of fit of path analysis:
Chi-square statistics: Non-significant chi-square value in path analysis shows the goodness of fit model. Sometimes, chi-square statistics is significant. However, we still have to test one absolute fit index and one incremental fit index.
Absolute fit index: RMSEA: An absolute fit index using 90% confidence interval for RMSEA should be less than 0.08 for a goodness of fit model.
Increment fit index: CFI, GFI, NNFI, TLI, RFI and AGFI, etc. are some incremental fit indexes, which should be greater than 0.90 for a goodness of fit model.
Modification indexes: Modification indexes (MI) may be used to add arrows to the model. The larger the MI, the more arrows will be added to the model, which will improve the model fit.
Assumptions in Path analysis:
Linearity: In path analysis, relationships should be linear.
Interval level data: In path analysis, data should be at interval scale.
Uncorrelated residual term: In path analysis, error term should not be correlated to any variable.
Disturbance terms: In path analysis, disturbance terms should not be correlated to endogenous variables.
Multicollinearity: In path analysis, low multicollinearity is assumed. Perfect multicollinearity may cause problems in the path analysis.
Identification: In path analysis, the path model should not be under identified. Exactly identified or over identified models are good for path analysis.
Adequate sample size: Kline (1998) recommends that the sample size should be 10 times (or ideally 20 times) as many cases as parameters.
Source: http://www.statisticssolutions.com/methods-chapter/statistical-tests/path-analysis/
Confirmatory factor analysis
Confirmatory factor analysis (CFA) is a multivariate statistical procedure that is used to test how well the measured variables represent the number of constructs. Confirmatory factor analysis (CFA) and exploratory factor analysis (EFA) are similar techniques, but in exploratory factor analysis (EFA), data is simply explored and provides information about the numbers of factors required to represent the data. In exploratory factor analysis, all measured variables are related to every latent variable. But in confirmatory factor analysis (CFA), researchers can specify the number of factors required in the data and which measured variable is related to which latent variable. Confirmatory factor analysis (CFA) is a tool that is used to confirm or reject the measurement theory.
Terms and concepts in confirmatory factor analysis (CFA):
Theory: In confirmatory factor analysis (CFA), theory is a systematic set of causal relationships that provide the comprehensive explanation of a phenomenon.
Model: In confirmatory factor analysis (CFA), model is a specified set of dependant relationships that can be used to test the theory.
Path analysis: In confirmatory factor analysis (CFA), path analysis is used to test structural equations.
Path diagram: In confirmatory factor analysis (CFA), the path diagram shows the graphical representation of cause and effect relationships of the theory.
Endogenous variable: In confirmatory factor analysis (CFA), endogenous variables are the resulting variables that are a causal relationship.
Exogenous variable: In confirmatory factor analysis (CFA), exogenous variables are the predictor variables.
Confirmatory analysis: In confirmatory factor analysis (CFA), confirmatory analysis is used to test the pre-specified relationship.
Cronbach’s alpha: In confirmatory factor analysis (CFA), Cronbach’s alpha is used to measure the reliability of two or more construct indicators.
Identification: In confirmatory factor analysis (CFA), identification is used to test whether or not there are a sufficient number of equations to solve the unknown coefficient. In confirmatory factor analysis (CFA) identifications are of three types: (1) underidentified, (2) exact identified, and (3) over-identified.
Goodness of fit: In confirmatory factor analysis (CFA), goodness of fit is the degree to which the observed input matrix is predicted by the estimated model.
The following are the procedures involved in confirmatory factor analysis (CFA):
1. Defining individual construct: In confirmatory factor analysis (CFA), first we have to define the individual constructs. In confirmatory factor analysis (CFA), the first step involves the procedure that defines constructs theoretically. This involves a pretest to evaluate the construct items, and a confirmatory test of the measurement model that is conducted using confirmatory factor analysis (CFA), etc.
2. Developing the overall measurement model theory: In confirmatory factor
analysis (CFA), we should consider the concept of unidimensionality between construct error variance and within construct error variance. At least four constructs and three items per constructs should be present in the research.
3. Designing a study to produce the empirical results: In confirmatory factor analysis (CFA), the measurement model must be specified. In confirmatory factor analysis (CFA), most commonly, the value of one loading estimate should be one per construct. In confirmatory factor analysis (CFA), two methods are available for identification. The first is rank condition, and the second is order condition.
4. Assessing the measurement model validity: In confirmatory factor analysis (CFA), assessing the measurement model validity occurs when the theoretical measurement model is compared with the reality model to see how well the data fits. In confirmatory factor analysis (CFA), to check the measurement model validity, the number of the indicator helps us. For example, in confirmatory factor analysis (CFA), the factor loading latent variable should be greater than 0.7. Chi-square test and other goodness of fit statistics like RMR, GFI, NFI, RMSEA, SIC, BIC, etc., are some key indicators that help in measuring the model validity in confirmatory factor analysis (CFA).
Confirmatory factor analysis (CFA) and statistical software: Usually, statistical software like AMOS, LISREL, EQS and SAS are used for confirmatory factor analysis (CFA). In AMOS, visual paths are manually drawn on the graphic window and analysis is performed. In confirmatory factor analysis (CFA) in LISREL, confirmatory factor analysis (CFA) can be performed graphically as well as from the menu. In SAS, confirmatory factor analysis (CFA) can be performed by using the programming languages.
Source: http://www.statisticssolutions.com/methods-chapter/statistical-tests/confirmatory-factor-analysis/
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