Some variables increase, some decrease, etc. You are observing this natural effect. Follow the song by KANSAS, "Carry on my wayward son". Remember to review regression coefficient meaning. Best wishes, David Booth

BTW Googler Path Analysis and Seawall Wright (from my hometown high school, GHS, believe).

The negative loadings would point to some indicators of the same factor being negatively correlated (reverse coded). It is not a problem per se as long as those correlations make sense and the indicators can still be meaningfully viewed as measures of the same latent variable. The standardized path coefficients (partial regression coefficients) > |1| point to multicollinearity and/or suppression effects as in conventional linear regression analysis. Are some of your factors that serve as predictors (topographical, physical, chemical) of the N2O outcome very highly correlated? What is the R^2 for N2O?

Also, you have a lot of correlated errors. Are all those theory-driven or were they empirically derived (e.g., based on modification indices)? Correlated errors can have a substantial impact on the factor measurement models and their interpretation.

Hello Waqar,

beyond what Christian already said, I have some problems understanding the latent variable. It seems that in your model, these are rather categories but not underlying common causes.

If a (measurement) model is substantially misspecified, you'll get bogus effect estimates.

HTH

--Holger

Thank you for the detailed answer Christian Geiser .

Yes there are some variables which are highly correlated. I tested multicollinearity and removed highly correlated variables.

The correlations were mainly based on modification indices, however, these are also supported by theory.

Holger Steinmetz I tried to extract variables using principal axis rotation, the factors I obtained from PAR were mixture of categories (e.g. topography, physical, chemical and biological). However, I want to keep these categories as latent variables. Is this possible? Or I have to use the factor analysis using principal axis factoring or other extraction methods and decide the latent variables (which are mixture of all categories).

Thanks

Dear Waqar

From your model and results:

to the best of my knowledge it is unacceptable to covary error terms with other error terms that are not part of the same factor ( in your model : e1 and e9 , e2 and e6, etc).

You should not covary errors of the items relating to one variable to the errors of items relating to another variable

Dear Waqar, in your model, the factor loadings of the two-item-constructs seem to indicate that you did not set the factor loadings to be equal. This is necessary, because measurement models with only two indicators are not identified. Then, factor loadings of both indicators will be of the same sign and size.

Error covariances across different factors are generally okay, if there is the theoretical justification for including them in the model. In your case, can you justify these relationships? I wonder.

Hoewer, I have a general problem with your model regarding the measurement models. I wonder whether the measurement models should be rather formative than reflexive. That means that the arrows should be reversed, i.e., pointing to the construct and not pointing from the construct to the indicators. For me, it would make sense if Slope and Landform constitute the common construct and not vice versa.

HTH, Karin

Dear Karin Schermelleh-Engel

am I correct in assuming that if one forced the two loadings of a two-item-construct to be equal that the model would be over-identified (i. e. actual testing of the model) because the amount of empirically available information (3) ((n*(n+1)/2)) is greater than the number of estimated parameters (2 = one factor loading and one residual variance)?

One follow-up question if I may: Provided that I want to use a two-item-construct only in combination with other over-identified constructs, is it necessary to hold the factor loadings of the two-item-construct equal? On its own, it is not identified, but in combination with other factors it can "borrow" information from those to make it work anyway.

Thank you in advance for your reply.

Best

Marcel

Dear Christian Geiser

I really appreciate your insightful response, however, if I had a latent factor consisting of indicators, some of which are coded from "low" to "high" while others are coded from "high" to "low", would that not cause the latent mean of that factor to become uninterpretable? Typically, we recode all items in the same direction prior to any calculations to avoid confusion.

Many thanks.

Best

Marcel

Marcel, with the factor loadings set equal the model is just identified, because you have to estimate two error variances and one factor loading, if the latent variance is fixed to zero, and you have three empirical variances/covariance. Of course, such a small model could "burrow" some information from other measurement models if they are correlated with the small model. In this case here, there are three non-identified models, and as the parameter estimates look quire weird, I would first set the loadings of two-indicator models to be equal and have a look at the results.

Kind regards, Karin

Marcel Grieger It is not strictly necessary to recode the items. However, sometimes when you have indicators that are keyed in opposite directions, this can lead to convergence problems due to the different signs of the loadings. Recoding (such that all items become positively correlated) often solves this problem (because all loadings are positive after recoding).

The mean of the latent variable is still identifiable and interpretable, even when items are keyed in different directions and are not recoded (i.e., when some have negative loadings). The mean of the latent factor can be identified by selecting a reference indicator/item for which the intercept is fixed to 0 and the loading is fixed to 1. Then, the mean of the latent variable is identified via the mean of this reference variable. Of course, the latent mean changes when you pick a different reference item (it is not uniquely defined unless you have strictly tau-equivalent measurements, i.e., equal loadings and intercepts across items). But the mean as such remains interpretable as the mean of the reference variable.

Contrary to Karin Schermelleh-Engel 's recommendation, I would not generally recommend setting the loadings equal in 2-indicator multifactor models unless the measured variables/indicators/items can be assumed to be essentially or strictly tau-equivalent based on prior research or theory (i.e., if they are measured on the same scale with the same units of measurement and have the same item discrimination). Setting the loadings equal within the same factor implies the (potentially untestable) assumption of (essential or strict) tau-equivalence. If the items are not essentially or strictly tau-equivalent (meaning if they don't have the same units of measurement and/or same item discrimination), then setting the loadings equal may induce potentially untestable model misspecification and parameter bias. A congeneric measurement model with 2 (or more) factors, 2 indicators per factor, and different loadings across indicators is overidentified as long as each factor has a correlation > |0| with at least one other factor in the model. If the loadings differ across variables within a given factor, it is better in my opinion to leave them free (not set equal) as long as there are no other problems with the model.

That being said, Karin Schermelleh-Engel is of course right that a single factor model with two indicators and different loadings is not identified in isolation (i.e., without other variables).

Thank you everyone for the answers. Your comments really helped me to understand the SEM. Additionally, I took an online course + watched some you tube tutorials and read a lot about EFA and CFA.

I re analyzed my data starting from Pearson correlation and collinearity tests. I removed all variables with low tolerance, high VIF and high Pearson correlations values to reduce collinearity.

Then I analyzed rest of the factors using Principal component analysis using principal axis factoring extraction method with Oblimin rotation.

At this step, I again removed variables with low communalities, and cross loadings.

At last I conducted SEM using variables in PCA analysis. Finally, I got a nice model explaining my direct, indirect and total effects. I got significance levels using bootstrap option. That was the whole purpose of mine to determine the direct and indirect impact of landscape on inorganic N, denitrifiers and N2O emissions.

The final model is attached.

I once again Thank everyone for being supportive.

Thanks

Dear Christian Geiser

thanks a lot for your thorough response. Now I know that by recoding the indicators in the same direction we err on the side of caution. As far as the latent mean is concerned, I will remember that "the mean as such remains interpretable as the mean of the reference variable". I had never thought about that.

With regard to forcing factor loadings to be equal in a two-item-factor, we had better avoid factors like that altogether. I am aware that sometimes it cannot be helped, but there is also content validity to be considered which may be called into question with only two indicators present.

Lastly, I watched your YT video on latent state-trait models. Very insightful (for non-statisticians like me). Looking forward to more content in the future.

Best

Marcel

Negative factor loading? Need to reverse coding for that particular item.

Negative factor loading? Need to reverse coding for that particular item.

Negative factor loading? Need to reverse coding for that particular item.

Negative factor loading? Need to reverse coding for that particular item.

Negative factor loading? Need to reverse coding for that particular item.

I am disappointed that I am late for the party - a very interesting discussion for someone trying to understand SEM like myself. Waqar Ashiq I guess you are done with your study (it's impressive that you had to read widely and eventually improved your model).

Your question of negative loadings has been answered from the discussion above, I suppose. After looking at your two models, I have some questions, perhaps some people who are part of the discussion will clarify here ( Zainudin Awang , Christian Geiser , Marcel Grieger , Karin Schermelleh-Engel , David Eugene Booth )

I will refer to your initial model as Model 1 and the revised model as Model 2.

1. On Model 1, why did you include an error term on the Topographical latent independent variable (exogenous)? I think all the other latent variables should have an error term except this one.

2. Just like the above point raised, on Model 2, there should be no error term on the Landscape latent exogenous variable. Waqar Ashiq , I will be glad to get a source that justifies an error term on an independent latent variable.

3. On Model 1, I see many error terms of observed variables covariated while they form part of different latent variables. For example, e1 is covariated with e9 while they form part of two different latent variables Topographical and Biological respectively. I agree with what Imtiaz Ahmad mentioned. However, covariating e1 and e2 is appropriate since they are both under the latent variable Topographical.

4. Is it advisable to use 2 items per latent variable in a SEM model (like in both models above)? I read somewhere that 3 or more are better.

5. In Model 1, independent latent variables are not covariated. Is it optional to covariate independent latent variables?

I listened to a course on YouTube by Saeed Sharif: https://www.youtube.com/watch?v=-rGIRIPgeWY&list=PLdQI483_ZTKzhaaIGjswUxkHNAbX1Qi78&index=5&ab_channel=saeedsharif

I agree with Prof Zainudin Awang, if there are negative worded items on the instrument, you need to record them. Thank you

*recode them