AMOS - Science topic

A chi-square value that is more than five times as large as its degrees of freedom points to substantial misfit/misspecification of your model. I don't think that non-normality alone accounts for this rather poor fit. Your model is quite large with many indicators and many factors. The poor chi-square fit indicates that there may be some inhomogeneities of the indicators (violations of unidimensionality). I would inspect standardized covariance residuals to examine which covariances are not well explained by your model.

Puja Vora Thanks for reaching out. I hope you had a joyous break. Yes, I am still unable to figure it out.

Thank you Christian Geiser

Hello,

Pls check for Prof. James GASKIN's tutorials on YouTube.

Also, google for gaskin's plugins for AMOS.

Although, Gaskin tilts more towards SmartPLSnowadays

Applying a linear constraint on intercepts in SPSS AMOS can be challenging due to its syntax limitations for certain custom constraints. However, it is possible to impose constraints using the Constraints feature available in AMOS. Here's how you can address this:Steps to Apply a Linear Constraint on Intercepts in AMOS Define a New Parameter for the Constraint:Instead of directly placing constraints on the intercepts, define a new parameter that represents the relationship between the two intercepts. For example, if the intercepts are β1\beta_1β1​ and β2\beta_2β2​, and you want to impose a constraint β1=β2\beta_1 = \beta_2β1​=β2​, you can define a new parameter and set it equal for both intercepts. Modify the Path Diagram:Open your AMOS model in the graphical interface. Right-click on the intercept of the first variable, and assign it a parameter name (e.g., Intercept1). Do the same for the second intercept (e.g., Intercept2). Add the Constraint:Click on Plugins in the AMOS toolbar and select Constraint Editor. In the Constraint Editor, you can write an equality constraint (e.g., Intercept1 = Intercept2) or a more complex linear constraint, such as β2=k⋅β1\beta_2 = k \cdot \beta_1β2​=k⋅β1​, where kkk is a constant. Save and apply the constraint. Run the Model:Execute the analysis after setting the constraint. AMOS will use this additional constraint during parameter estimation. Tips for Syntax-Based Constraints Although AMOS syntax is limited, you can specify equality constraints directly using parameter names:For example, if you assign Intercept1 and Intercept2 as parameter names, adding Intercept1 = Intercept2 in the syntax window should work. Alternative Approach: Using R (lavaan) for Greater Flexibility If AMOS proves too rigid, consider switching to R with the lavaan package for structural equation modeling. In lavaan, you can easily specify such constraints in the model syntax: R

model <- ' # Regression equations y1 ~ x1 + intercept1 y2 ~ x2 + intercept2 # Constraint intercept1 == intercept2 ' fit <- sem(model, data = your_data) summary(fit)

This approach provides more flexibility and allows you to define constraints directly within the syntax.

You should try R (laavan)

Any ideas on how to write the DISCUSSION section when the results of your model analysis do not fit to the data, and only one hypothesis seem statistical significant? Thank you! It's my first time to do research in the social science with SEM. I am not an expert!!

As far as I recall, AMOS by default does not report indirect effects along individual paths when there is more than one indirect path between two factors/variables (e.g., in a parallel mediation model). Did you use user-defined estimands to get the estimates of the three indirect effects? If yes, maybe the syntax error is in the code defining these estimands, not in the model.

I think AMOS is included in recent versions of SPSS

Perhaps the issue is that you specified an error term (e1) for your independent/exogenous variable (Cognitive). Exogenous variables have no associated error terms/error variances as parameters in path models. Only mediating/dependent/endogenous variables have error terms/error variances.

Is this the calculation we must Amos does? Q² = 1 - \frac{SS_{res}}{SS_{total}}Q2=1−SStotal​SSres​​

The most accurate tool to check moderation is SmartPLS software. In Amos, the model is also drawn, but the moderation evaluation is done in separate parts. For this reason, SmartPLS provides more accurate results for each type of moderator with simultaneous processing.

Yes, the signs of the direct and indirect effects do matter when calculating the total effect in mediation analysis. Here's how the signs influence the total effect:

Breakdown of Effects in Mediation:

How Signs Matter:

Example:

Interpretation:

No, because when model fit is poor, model-implied estimates of reliability and validity may be biased--they are based on an incorrect model.

In snowball sampling, true statistical representativeness is difficult to achieve due to its non-random nature. While there isn’t a specific statistical test to confirm representativeness, researchers can:

1. Compare the sample’s characteristics with known population data (if available) to assess representativeness.

2. Start with multiple initial participants (“seeds”) to increase diversity.

3. Apply statistical adjustments like post-stratification weighting to better align the sample with the population.

You can see www.Stats4Edu.com

To second Christian Geiser answer: it is a very strong assumption to omit paths or covariances. It means that you imply this associations to be zero. Any non-zero association in the data will contribute to a misfit of the model. Such strong assumptions should be backed up by theory, otherwise it is reasonable to model this possible relations.

Hi Esam.

See these videos attached and check if they can help you.

I think the heaviest one (34.7 MB) should be more useful but the shortest can indicate chi-square test, which can be useful too.

Regards.

please stop posting chatGPT or otherwise AI generated text, especially without explicitly mentioning it!! This is very unscientific!

Andrei Mikhailov please tell, are you interested in moderation of latent variables or manifest variables?

Hi. Same opinion as Bhumika Bunkar. Please provide more information in such a way we can help you.

The purchase options for AMOS and other IBM software are a bit complex and overly expensive. However, if you are affiliated with an academic institution (as a student or faculty member), you can purchase through the vendors. This is a much cheaper and easier way.

https://www.ibm.com/products/spss-statistics/gradpack#vendors

You can also search for your local vendors. Again, your organization may already own this software for its constituents.

There are some illegal ways to obtain a license too. However, these are highly discouraged and considered as crime in most countries.

In addition to Christian's recommendation of removing by theoretical reasoning first, you could also use algorithmic approaches such as the ones described by Schroeders et al. (2016, here: 10.1371/journal.pone.0167110) or me and my colleague for specifically cross-cultural settings (10.1027/1614-2241/a000155), which I also implemented in an R-Package called stuart.

AMOS can indeed be used when the dependent variable is an observable variable, such as student grades, to measure performance. However, if the model does not run with the overall grade, several factors might be causing this issue. Potential reasons include data issues, model specification errors, or the necessity for the grades to be part of a larger latent construct within the structural equation model. To resolve this, ensure that the data are properly prepared, the model is correctly specified, and consider using grades as indicators of a latent performance construct if applicable. Additionally, check for multicollinearity, handle any missing values, and make sure all paths and relationships in the model are accurately defined. These steps can help troubleshoot and resolve the issues preventing the model from running correctly.

You guys may read this paper. It's very helpful: Marketing research using single-item indicators in structural equation models https://link.springer.com/content/pdf/10.1057/jma.2013.7.pdf

Hola , check here https://stats4edu.com/services/structural-equation-modeling/

See here https://stats4edu.com/services/structural-equation-modeling/

Check here https://stats4edu.com/services/structural-equation-modeling/

AVE measures the average amount of variance captured by each latent construct (in your case, Attitude). A higher AVE indicates that the items in your construct are measuring the underlying concept well. A commonly accepted threshold for AVE is 0.5 or higher, indicating that at least 50% of the variance in the observed variables is accounted for by the latent construct. Your AVE of 0.465 suggests that your Attitude construct is capturing a moderate amount of variance in your observed variables.

What did you exactly do to avoid the nonsesns negative X2, or C/min?

I repeat the same analysis hundreds of time adn nothing works. The effects are fine but the fit can not be computed.

Quite desperate!

Using SPS_AMOS, I received a huge negative X2 for my path analysis. What went wrong?

AMOS (Analysis of Moment Structures) is a popular software tool for structural equation modeling (SEM). While AMOS itself does not "generate" p-values or RMSEA values directly, it can compute these values as part of the analysis outputs. However, the accuracy and reliability of these values depend on various factors, including the model specification, sample size, and data quality.

Here are some considerations regarding p-values and RMSEA values in AMOS:

If you are experiencing specific issues with generating p-values or RMSEA values in AMOS 25, it may be helpful to review the model specification, data quality, and other factors mentioned above to troubleshoot the problem. Additionally, consulting resources such as user guides, forums, or contacting technical support for the software can provide further assistance in addressing any issues you encounter.

Hi Karan

1. No. In SPSS you could run a principal component analysis which is a model for causal indictors. In AMOS you could set up a model with causal indictors, although there will some restrictions - have a look at some more brilliant work by Bollen on this issue doi: 10.1037/a0024448

2. Yes, you could use principal component analysis to do an 'EFA' although this would not strictly be a factor analysis, and a CFA could be set up with causal indictors.

Once you have a measurement model set up, the ANOVA or MANOVA are not too difficult to specify by using dummy coded variables (and maybe products if you want interactions). Have a look at some of Richard Bagozzi's work from back in the day - it's brilliant.

My usual suggestion when there are questions on formative/reflective constructs is to read everything Ken Bollen has written on this - start with the 'Conventional Wisdom' paper, it's one of the best papers on measurement that has ever been written.

Bollen, K., & Lennox, R. (1991). Conventional wisdom on measurement: A structural equation perspective. Psychological Bulletin, 110(2), 305–314. https://doi.org/10.1037/0033-2909.110.2.305

1991 was a good year for the nerds!

Mark

Thank you. your response was very helpful

In Spss, by default there is only EFA and not CFA. So, if you need CFA, better to use someother softwares such as AMOS etc.

I think the reviewer is expecting you to provide examples of a few studies of a similar nature to show that your study is not just based on theory but is based on gaps in the existing literature. Therefore, I'd suggest you to search and include a few studies that examine the impact of training and development and performance appraisal on the competitive advantage of schools.

Hey Jaber,

I think you are comparing a statistical approach (PLS) to a specific software programme (AMOS) so I don't have an answer to which is 'best'. AMOS is used for standard covariance based latent variable modelling, and as such is hugely flexible and powerful. You get all the benefits of maximum likelihood estimation and model fit statistics. The downside is that you get maximum likelihood estimation and model fit statistics.

Looking at your proposed model I suspect that PLS may be an easier way to specify the 'causal' indicators, but I also suspect that reviewers would ask some tricky questions about why you didn't use a model model testing approach such as latent variable modelling, or SEM, or whatever you want to call it.

This is an intersting articale that applies both methods , and there is also a brilliant episode of the Quantitude podcast on PLS. The 'brilliant' was unnecessary as all episode of Quantitude are brilliant.

Mark

It is possible to use the same variable twice, once as a mediator and once as an independent variable. This methodology enables a more comprehensive examination of the connections inside the model.

For Reference:

https://www.statalist.org/forums/forum/general-stata-discussion/general/1350511-testing-mediation-between-10-independent-variables-and-1-dv-with-mixed

Only the residual (disturbance, error) terms can be correlated for endogenous (dependent) variables in a path/SEM model. The reason is that the covariance of endogenous variables is not a free parameter but a function of other free model parameters. You should be able to include covariances among the residual/error/disturbance (e) terms.

The indirect effect is positive because it is, by definition, equal to the product of two (in this case negative) path (regression) coefficients:

Indirect effect = (-.20)*(-.19) = .038.

The 95% confidence interval includes the value of zero though [.00, .09] and therefore, according to the CI, the indirect effect would not be statistically significant at the .05 level.

Any kind of causal interpretation is questionable, especially if you are dealing with non-experimental, cross-sectional data where X is not manipulated and X, M, and Y are measured at the same time point.

See:

Maxwell, S. E., & Cole, D. A. (2007). Bias in cross-sectional analyses of longitudinal mediation. Psychological Methods, 12(1), 23-44.

Maxwell, S. E., Cole, D. A., & Mitchell, M. A. (2011). Bias in cross-sectional analyses of longitudinal mediation: Partial and complete mediation under an autoregressive model. Multivariate Behavioral Research, 46(5), 816-841.

Hi Dr. Junsu,

From memory, I think the Hayes book (Introduction to Mediation, Moderation, and Conditional Process Analysis) mentions this issue. If you are dealing with a reviewer's comment, I would just explain the difference between a simple bivariate correlation versus a complex model, and how relationships can differ because of the inclusion of multiple other variables in a complex model.

Hope this information helps.

Kind Regards,

Lorcan.

When maximum likelihood (ML) estimation is used in covariance-based structural equation modeling (CB-SEM), multivariate normality is assumed. However, violations of normality are not necessarily problematic. Robust ML estimation methods (e.g., Satorra-Bentler correction) or bootstrapping (Bollen-Stine) can be used to adjust the model fit statistics and standard errors when variables are not normally distributed.

A CFI value of 0.88 does not indicate an adequate model fit, but the most important criterion would be the chi-square test of model fit. I'm assuming from the low CFI that the chi-square must be highly significant, indicating model misfit. You should re-examine your model to identify potential sources of model misspecification before moving on to more restricted invariance models that could only fit worse than your current model.

Dear Thameera Manju

It is not available for free, it is available on Amazon for $24.85

Therefore, I think there is a problem with sharing it or publishing parts of it publicly without the author’s consent.

Hello Karan,

you use the three groups as in any other kind of multigroup scenario. I don't know how this is dealt with in AMOS but you can easily find that out :)

With regard to the CFA, the essential question whether a respective set of items follow a common factor structure. Remember, the common factor model claims that all indicators are exchangeable reflections of the same underlying entity. In contrast you may have sets of items that comprise an index or aggregates. Hence think about first or misfit is guaranteed.

If the factor structure is plausible, you should incorporate the CFA as part of the multigroup approach which allows to test for measurement invariance (most notably metric invariance, that this equality of the loadings)

Best,

Holger

Hey Marwa

The GFI doesn't appear outside of LISREL because it doesn't work - it's way too liberal. Karl Joreskog tells a funny story that the early versions of LISREL only had the chi-square statistic and it was very unpopular because models were always rejected. He developed and implemented the GFI and every model fitted well, and LISREL became very popular. It's a good story, not sure how true it is.

This study shows that it's junk.

Shevlin, M., & Miles, J. N. V. (1998). Effects of sample size, model specification and factor loadings on the GFI in confirmatory factor analysis. Personality and Individual Differences, 25(1), 85–90. https://doi.org/10.1016/S0191-8869(98)00055-5

Mark

Myself, you may want to delete the variables from the analysis and tell the reader you did that. Having variables in your model which have no correlations with anything else will cause you to have a good fit to the independence null (which assumes no correlations) and therefore traditional fit indices like the TLI will not be as high. It depends on the context of your study, though. if these are variables that everybody in your area are using I would think you'd want to keep them in the model. Before you do that, though, be sure to scatterplot these variables against the other variables in the factor. maybe there are some problems with the variables (like nonlinear relationships or outlying observations) which are behind the low correlations. For what it's worth.

"Wrong" is very ambigious. It may be wrong from a theoretical standpoint, that you build a wrong model, which is not in accordance with your underlying theory. Wrong could also mean "bad fit", that you modeled it according to your theory, but the bad fit indicates that your data and theory do not fit very well. Or you did something technically wrong, so you specified something that should not be (e.g. items are on the wrong latent variable). Or wrong in the sense of "suboptimal", e.g. maximum likelihood estimators for ordinal items.

So please clarify!

It depends on why these negative loadings occur (i.e., is it plausible?) and what exactly they look like in the context of the entire model.

Think of the arrows as statements about causality. In your model you are saying "Brand Image causes Auditory", also "Auditory causes MAT" and so on. This is the normal approach in SEM with AMOS. You have observed variables, (MAT, MDE, MPE, etc) that are manifestations of unobserved, or latent, constructs (Auditor, Olfactory, etc). In your model, these unobserved constructs are themselves manifestations of a second-order latent construct, Brand Image.

So that is the theory that you are presenting in your model: your observed (or 'manifest') variables are a result of some other construct that we cannot measure directly, the latent construct Brand Image.

Your panel members believe that arrows - the causal links - should point to Brand Image from Auditory, Olfactory, etc. That would be to say that Auditory causes Brand Image (along with the other first-order latent constructs). You can do that only if you have separate independent measures of Brand Image. That is, where you can say that observed variables such as 'value for money', 'prestige', 'innovativeness', and so on (see Plumeyer et al. for many other examples) are manifestations of Brand Image.

Your model is not a structural model of causal relationships among constructs. It is a model where you propose that Brand Image, which we cannot observe directly, produces five perceptions (Auditory, Olfactory, etc., which we also cannot observe directly), and each of these is manifested by about seven observed variables.

This is not wrong as such. It could be useful if you want to show that your measures are good at measuring your constructs.

Having said that, you should also do the following:

* Present the standardised coefficients. This helps you and the reader understand how much stronger some coefficients are than others. Check the statistical significance of the coefficients from your constructs to your manifest variables. You will probably find that you can comfortably use just four or five manifest variables for each construct instead of the seven or eight that you have.

* Before including the second-order latent construct Brand Image to the model, check the measurement model. (correlate each of the first-order constructs with each other first-order construct, and then check the sign and strength of the coefficients to decide if you really need that observed variable in the model)

* Check for common-method bias and decide if you really need some observed variables.

There are lots of 'how-to' tutorials online and YouTube videos to show you how to do these, Shivam Bhardwaj

Good luck.

Reference:

Plumeyer, A., Kottemann, P., Böger, D. et al. Measuring brand image: a systematic review, practical guidance, and future research directions. Review of Managerial Science 13, 227–265 (2019). https://doi.org/10.1007/s11846-017-0251-2

In fact, the R lavaan package is also implemented in jamovi, which is also free. See https://semlj.github.io

The standardized indirect effect represents the relationship between an independent variable and a dependent variable through a mediating variable. It is a crucial measure as it helps us understand how much of the total effect can be attributed to this mediation process. Nevertheless, Amos does not provide a statistical test for its significance.

This limitation in Amos arises due to various reasons. Firstly, testing for significance requires estimating standard errors and calculating p-values, which are not available for the standardized indirect effect in Amos. Secondly, it is important to consider that significance testing may not always be appropriate or meaningful in all research contexts.

Despite this limitation, researchers can still interpret and discuss the magnitude and directionality of the standardized indirect effect observed in their SEM models analyzed using Amos. By focusing on effect sizes rather than statistical significance alone, researchers can gain valuable insights into their research questions and contribute to scientific knowledge.

Please see that whether the error term is added to all indicators; and please see that constraint (1) is assigned to the arrow, which is leading to a latent variable or construct. Later-on I had taken care of all these things and I got success.

Hi Charlotte,

can you show a path diagram with explanation of the variables involved. Strange negative effects ring the "collider bias" bell. Christian Geiser you pointed into the right direction although I found this paper here much more eye-opening:

Kim, Y. (2019). The causal structure of suppressor variables. Journal of Educational and Behavioral Statistics, 1076998619825679. doi:10.3102/1076998619825679

More on collider bias:

Elwert, F., & Winship, C. (2014). Endogenous selection bias: The problem of conditioning on a collider variable. Annual Review of Sociology, 40, 31-53. doi:10.1146/annurev-soc-071913-043455

Best,

Holger

The two programs use different statistical techniques: AMOS uses covariance based SEM, whereas SMART-PLS uses partial least squares. There is some critique concerning PLS and I would stick with the covariance based approach (but not necessarily with AMOS). But you have to know what your are doing and what is maybe more common in your field.

The G_Pers factor may be identifiable without fixing both paths (to CI and Willing) if at least one of the "formative indicators" of G_Pers is substantially correlated with the G_Pers factor (i.e., if at least one of the paths from the "formative indicators" is substantially different from 0). However, one of the reflective paths (to either CI or Willing) will still have to be fixed as far as I can tell. Otherwise, the G_Pers factor with a freely estimated residual variance (variance of e40 in your picture) will not be identified.

This is why I would think of the G_Pers factor as being a reflective (second-order) factor rather than a "formative" variable. Its identification and meaning is based on the reflective indicators (CI and Willing) rather than the "formative indicators." The "formative indicators" are merely observed predictor variables (covariates) of a second-order reflective factor.

The problem is not so much estimation/identification as it is interpretation. In my opinion, only reflective measurement can be considered "measurement" in a classical sense. That being said, you might consider using composites, which are clearly defined. See, for example, work by Joerg Henseler, Florian Schuberth, and colleagues on confirmatory composite analysis:

Yes, the P-value in Smaart Pis CB-SEM is reliable. It is calculated using the same statistical methods as other structural equation modeling (SEM) software.

The P-value is a measure of the statistical significance of a test. It is calculated by assuming that the null hypothesis is true and then computing the probability of obtaining a test statistic as extreme or more extreme than the one observed if the null hypothesis were true. A P-value less than 0.05 is generally considered to be statistically significant, meaning that there is a less than 5% chance of obtaining the observed results if the null hypothesis were true.

There are a few things to keep in mind when interpreting P-values in SEM:

Overall, the P-value in Smaart Pis CB-SEM is a reliable measure of the statistical significance of a test. However, it is important to keep the limitations of P-values in mind when interpreting them.

Here are some additional tips for interpreting P-values in SEM:

If you have any questions about interpreting P-values in SEM, you should consult with a statistician or other expert.

You can use Maximum Likelihood to estimate the parameters of your model and request to he Bollen Stine bootstrap to obtain robust standard errors and test statistics. (The standard errors and test statistics are most affected by data non-normality.)

Alamir Louro, thank you for responding to my request - and for having done so with so much detail. You are certainly right about SPSS being limited by providing the default of eigenvalues > 1 criterion for suggesting - and producing - the number of factors in a data set. At least, researchers can over-ride that and specify the number of factors they want to be extracted, perhaps on the basis of parallel analysis, scree plot, etc. However, it would be nice if a package produced parallel analysis as a matter of course.

It was generous of you to provide your email address. I might get in touch with you some day to have a bit of "joint experience" with factor analysis.

Thanks again.

That makes sense. Are you comparing the cross-lagged panel (auto)regression (path) coefficients to zero-order correlations? This could be part of the issue (explain the "discrepancy"/low autoregressive stability coefficient). Regression coefficients are not equal to zero-order (bivariate) correlations. The regression coefficients take the correlation with other independent variables into account. This may explain why the autoregressive "stability" coefficients in your model look very different from the zero-order correlations. It is impossible to know without looking at your data and model in more detail.

The model fit does not look completely horrible at first sight but the chi-square test is significant and the RMSEA value is a bit high. I would take a look at model residuals and/or modification indices to find out where the model may be misspecified.

I looked at the SPSS website and found this: "Amos is included in the Premium edition of SPSS Statistics (except in Campus Edition, where it is sold separately)."

It sounds like you will need to contact SPSS support to get a definitive answer.

Hey Hua (Catherine) Xin ,

It depends on your undertstanding about a formative construct. If you regard it as a latent variable, you can model a causal-formative measurement model, see e.g., Bollen & Bauldray (2011). CB-SEM is eminently suitable for that. If you regard a formative construct as a composite that is composed of other variables, you can employ the Henseler-Ogasawara specification which allows for flexibly modeling composites in CB-SEM, see e.g., Schuberth (2021), Yu et al. (2023).

HTH

Best regards,

Florian

References:

K. A. Bollen and S. Bauldry, “Three Cs in measurement models: Causal indicators, composite indicators, and covariates,” Psychological Methods, vol. 16, no. 3, pp. 265–284, 2011, doi: 10.1037/a0024448.

F. Schuberth, “The Henseler-Ogasawara specification of composites in structural equation modeling: A tutorial,” Psychological Methods, 2021, doi: 10.1037/met0000432.

X. Yu, F. Schuberth, and J. Henseler, “Specifying composites in structural equation modeling: A refinement of the Henseler-Ogasawara specification,” Statistical Analysis and Data Mining, vol. 16, no. 4, pp. 348–357, 2023, doi: 10.1002/sam.11608.

Dawit Negussie : You may find this article useful:

The new SmartPLS 4 release (https://www.smartpls.com/) offers PLS-SEM but also CB-SEM (like IBM SPSS Amos) - and many other methods such as regression analysis, path analysis and PROCESS, necessary condition analysis, logistic regression, and confirmatory factor analysis (via CB-SEM projects).

Hi,

Check this out :

Hi,

You check this out :

Yes, you can use AMOS and PLS-SEM in the same study. However, it is important to ensure that the methods are appropriate for the research question and the specific characteristics of the data

Endogeneity refers to a situation in which a variable in a statistical model is correlated with the error term or disturbance term. This correlation can lead to biased and inconsistent parameter estimates, making it challenging to establish causal relationships between variables. Endogeneity often arises in observational or cross-sectional research designs, where the researcher cannot control for all possible confounding factors.

To address endogeneity in your analysis using survey data in SPSS/AMOS, you can consider implementing the two-stage least squares (2SLS) method. This method is commonly used in econometrics to address endogeneity by using instrumental variables. Here is a step-by-step procedure:

In AMOS, which is a software primarily used for structural equation modeling (SEM), you can also address endogeneity using a similar two-stage approach. You would specify a measurement model for your latent variables and a structural model for the relationships between the latent variables. You can include instrumental variables as exogenous variables in your structural model to account for endogeneity.

It's important to note that implementing the 2SLS method or addressing endogeneity, in general, requires careful consideration of the specific research context, availability of instrumental variables, and the assumptions underlying the method. It is recommended to consult with a statistician or econometrician who can guide you through the process and ensure its appropriate application to your specific research design.

For regression analysis, there is also this, with a new algorithm:

You can try it for 25 days. Comments welcome!

To add a published paper to your ResearchGate profile, you need to:

Alternatively, you can add a publication page to your profile by clicking the Add new button at the top right-hand corner of any ResearchGate page. I hope that helps!

Structural equation modeling (SEM) is a method that allows researchers to test complex hypotheses about the relationships among observed and latent variables (Kline, 2015). Observed variables are those that can be measured directly, such as test scores or survey responses. Latent variables are those that cannot be measured directly, such as intelligence or academic achievement. SEM involves specifying a model that represents the causal structure of the variables and estimating the parameters of the model using data. One of the advantages of SEM is that it can provide information about the fit of the model to the data, as well as the modification indices that suggest how the model can be improved (Byrne, 2016).

One of the questions that may arise when using SEM is whether it is appropriate to connect an observed variable and an error variable if the output suggests it in modification indices. An error variable is a latent variable that represents the measurement error or unexplained variance of an observed variable. Connecting an observed variable and an error variable means adding a path between them in the model, which implies that there is a direct effect of one variable on another. This may not make sense theoretically or conceptually, as error variables are usually assumed to be independent of other variables in the model. Therefore, connecting an observed variable and an error variable may not be a good practice in SEM, unless there is a strong justification for doing so based on substantive knowledge or previous research (Brown, 2015).

With a single indicator, the unstandardized loading must be fixed to 1 and the error variance must be either fixed to zero (assuming/implying perfect reliability of the indicator--not a very realistic scenario) or to a theoretically meaningful value that corresponds to your "best guess" as to how much error variance there is in the observed variable. The estimate of the error variance can sometimes be derived from reliability estimates (but be careful when using reliability estimates from prior studies as they may not apply to your sample/population).

With known reliability, the error variance for an observed variable (indicator) Y can, according to classical test theory, be computed as

Var(error) = Var(Y)*(1 - reliability).

It is not meaningful to estimate the loading of a single indicator. The unstandardized loading must be fixed to one for identification. The standardized loading will be "estimated" but will trivially correspond to the square root of the reliability coefficient when fixing the error variance according to the formula above. So there is no new information there.

Hi Ann,

why not incorporate both goals and add the cross-group constraint ("structural equivalence") on the effects after metric invariance has been tested. This would fit nicely into one approach and avoid the use of path analysis (which is a bid strange as you had latent variables in the first approach anyway).

Best,

Holger

My guess is that the first p value is based on a regular theoretical/asymptotic standard error, whereas the second one is based on bootstrapping, which is a different methodology for finding a p value empirically based on resampling rather than asymptotic theory.

What do you mean when you say some of the questions are not "valid" in EFA but are in CFA?

can second order be changed to first order in sem

Hello Irfan,

When an IV->DV relationship is zero or near-zero, and the IV->Mediator->DV relationship is non-zero, then you have evidence for full or nearly full mediation, at least for your sample.

Good luck with your work.

With the latest SmartPLS release, you can run both PLS-SEM and CB-SEM (like Amos): https://www.smartpls.com/downloads