In the final throes of a PhD. I have viewed numerous SPSS and AMOS based videos. Thank you for your time in presenting such informative discussions, which I have cited accordingly.
Thank you, dear professor, super video I have a question: why estimate the variance of endogenous variables? Because the objective of a path analysis model is the estimates of three types of parameters: The paths, The covariances between the exogenous variables, and the variances of the exogenous variables. To determine the direct, indirect, and total effects between the variables. To avoid the Heywood cases, it is better to fix the variance of the endogenous variable to its empirical variance. And thus the parameters (Psi) variance of disturbance is constrained parameters not free?
Hi, thanks for your great videos! I was wondering, what approach would you recommend to get an over-identified model that makes theoretical sense? Fixing a path value doesn't make sense as it is what we want to estimate. On the other hand, having a just identified model, and thus no model fit indicators is not acceptable either. Many thanks.
Hi Arthur. Thanks for your question - it's an important one! So here's my response: The decisions concerning whether or not to fix parameters really should depend largely on the type of model you are trying to test as well as various substantive considerations other than just ensuring that the model is over-identified (as opposed to just-identified). Consider the following example: Even though no one really does this in practice, you could run a regression analysis through SEM. After specifying the model's parameters, you'll end up with a just-identified model (as you'd be estimating the variances and covariances for the IV's, the path coefficients, and the variance of the residuals for the endogenous variable). In this circumstance, there is really no logical fixing of any of these values, so the model will remain just-identified (and so the fit indices - e.g., RMSEA, CFI, etc. - will not be useful in judging its overall fit). Now, on the other hand, if you had an apriori reason for fixing one of those parameters to a given value (e.g., you have reason to believe the population regression slope for a predictor is say, b=.20), then fixing that value (instead of estimating the parameter) will result in 1 added degree of freedom. So, the model would be over-identified in that case. Obviously, this is a very unusual case - but it might be a reason for one could choose to fix a regression coefficient (again if you are testing the fit of the model where the other coefficients are estimated but you have reason to believe the population parameter is .20). At this point it is worth pointing out that we often fix parameters in models without actually thinking about them in any great depth. For instance, the path from the residual error in the above-mentioned regression model (and for all endogenous variables in path models, CFA models, etc) is fixed to 1. This is to scale the variance of the errors in relation to the manifest endogenous variable. Without fixing this parameter, the model will be unidentified (which is a problem for sure). Similarly, in the context of CFA, we scale the latent variables by either (a) fixing one factor loading to 1 (so that the latent variable is scaled in reference to one of its indicators) or (b) fixing the variance of the latent factor to 1 (resulting in a variance estimate of 1). The choice to fix these parameters in this case is not about moving from a just-identified model to an over-identified model. These restrictions are placed in the models to allow for proper estimation. Moreover, you can think of the decision to NOT include a path from one variable to another in a path model (for instance) as essentially fixing that potential relationship between two variables to 0. In this case, the decision to not specify a path is based on theory, not the issue of identification. One thing you mentioned about "having a just identified model" and "no model fit indicators is not acceptable": I would not necessarily say that is true that a just identified model is "unacceptable". It is true that you can't use standard measures of goodness of fit (like RMSEA, CFI, etc.) to evaluate overall model fit. But a just-identified model is not inherently "wrong" or "bad". It just means that you can't evaluate fit using those conventional indices [unfortunately some folks might ASSUME is an indication of a "wrong" or "bad" model; but I can't other people's perceptions, right?]. You can still evaluate the fit of a just-identified model using many of the same indicators you are used to with regression (e.g., significance of path coefficients, R-square values, etc.). [We do that every day using standard OLS regression!] So, simply put - a model is not misspecified because of it being just-identified. It is misspecified to the extent that the model fails to adequately represent the true relations among the variables. The issue of the model being just-identified is that you can't evaluate the fit of the model using certain tools (e.g., the fit indices). That said, it is worth noting that sometimes folks make models unnecessarily complex and then they run into a model that is either just-identified or under-identified. But in these cases, the identification problem comes more from a lack of adequate conceptualization of the relationships involving the variables (resulting in a tendency to specify a model where everything predicts everything - which looks like spaghetti in a diagram!). However, I would point out that you can also have the same problem with spaghetti and still have an over-identified model too. Indeed, you can have an overidentified model that still doesn't say anything useful and/or horribly misspecified! Obviously, in this case, you are able to judge the degree of overall model misspecification using the fit indices. One final thing: I don't want to give you the impression that model identification is unimportant when judging model fit. You certainly have more information regarding model fit when you have specified an over-identified model as opposed to a just-identified model. My main point is that there may be times when a just-identified model is theoretically logical and defensible and that making tweaks to the model by fixing or removing parameters just to achieve an over-identified model makes no sense. So there you have it. I appreciate the question because I'm sure that many others have the same question (hell, I had the same question when learning about SEM :) I hope this has made this a little less cloudy! Best wishes!
Hi Mike, thank you so much for your very detailed answer! In my model, I fixed one of my covariances to 0 as I know that those variables are not correlated, which makes the model over-identified. I guess that works. At any rate (as you like to say haha), "You can still evaluate the fit of a just-identified model using many of the same indicators you are used to with regression (e.g., significance of path coefficients, R-square values, etc.). [We do that every day using standard OLS regression!]": I haven't look at it this way, but it definitely makes sense :) Many thanks
If this was a "2-step" path model where age & years predict 2 intermediate variables, which predicts deference...would the variances for these intermediate variables be considered parameters? (assuming no covariance between the two intermediate variables)
In my modell I won't get any numbers because it says it is unidentified. I becomes identified when I give one of the paths from the indicators describing a construct to the construct a regression weight of 1. Is there a way I can get numbers without fixing them? If not, how do I choose the right variable to fix to 1? Thank you!
In the final throes of a PhD. I have viewed numerous SPSS and AMOS based videos. Thank you for your time in presenting such informative discussions, which I have cited accordingly.
This particular video is of great help for me to my current assignment. Thank you Mike
you are the kindest gentleman on the internet my good sir you have assured that i shall acquire a masters degree tyvm
Thank you, dear professor, super video I have a question: why estimate the variance of endogenous variables? Because the objective of a path analysis model is the estimates of three types of parameters: The paths, The covariances between the exogenous variables, and the variances of the exogenous variables. To determine the direct, indirect, and total effects between the variables. To avoid the Heywood cases, it is better to fix the variance of the endogenous variable to its empirical variance. And thus the parameters (Psi) variance of disturbance is constrained parameters not free?
Hi, thanks for your great videos! I was wondering, what approach would you recommend to get an over-identified model that makes theoretical sense? Fixing a path value doesn't make sense as it is what we want to estimate. On the other hand, having a just identified model, and thus no model fit indicators is not acceptable either. Many thanks.
Hi Arthur. Thanks for your question - it's an important one! So here's my response:
The decisions concerning whether or not to fix parameters really should depend largely on the type of model you are trying to test as well as various substantive considerations other than just ensuring that the model is over-identified (as opposed to just-identified). Consider the following example: Even though no one really does this in practice, you could run a regression analysis through SEM. After specifying the model's parameters, you'll end up with a just-identified model (as you'd be estimating the variances and covariances for the IV's, the path coefficients, and the variance of the residuals for the endogenous variable). In this circumstance, there is really no logical fixing of any of these values, so the model will remain just-identified (and so the fit indices - e.g., RMSEA, CFI, etc. - will not be useful in judging its overall fit). Now, on the other hand, if you had an apriori reason for fixing one of those parameters to a given value (e.g., you have reason to believe the population regression slope for a predictor is say, b=.20), then fixing that value (instead of estimating the parameter) will result in 1 added degree of freedom. So, the model would be over-identified in that case. Obviously, this is a very unusual case - but it might be a reason for one could choose to fix a regression coefficient (again if you are testing the fit of the model where the other coefficients are estimated but you have reason to believe the population parameter is .20).
At this point it is worth pointing out that we often fix parameters in models without actually thinking about them in any great depth. For instance, the path from the residual error in the above-mentioned regression model (and for all endogenous variables in path models, CFA models, etc) is fixed to 1. This is to scale the variance of the errors in relation to the manifest endogenous variable. Without fixing this parameter, the model will be unidentified (which is a problem for sure). Similarly, in the context of CFA, we scale the latent variables by either (a) fixing one factor loading to 1 (so that the latent variable is scaled in reference to one of its indicators) or (b) fixing the variance of the latent factor to 1 (resulting in a variance estimate of 1). The choice to fix these parameters in this case is not about moving from a just-identified model to an over-identified model. These restrictions are placed in the models to allow for proper estimation. Moreover, you can think of the decision to NOT include a path from one variable to another in a path model (for instance) as essentially fixing that potential relationship between two variables to 0. In this case, the decision to not specify a path is based on theory, not the issue of identification.
One thing you mentioned about "having a just identified model" and "no model fit indicators is not acceptable": I would not necessarily say that is true that a just identified model is "unacceptable". It is true that you can't use standard measures of goodness of fit (like RMSEA, CFI, etc.) to evaluate overall model fit. But a just-identified model is not inherently "wrong" or "bad". It just means that you can't evaluate fit using those conventional indices [unfortunately some folks might ASSUME is an indication of a "wrong" or "bad" model; but I can't other people's perceptions, right?]. You can still evaluate the fit of a just-identified model using many of the same indicators you are used to with regression (e.g., significance of path coefficients, R-square values, etc.). [We do that every day using standard OLS regression!] So, simply put - a model is not misspecified because of it being just-identified. It is misspecified to the extent that the model fails to adequately represent the true relations among the variables. The issue of the model being just-identified is that you can't evaluate the fit of the model using certain tools (e.g., the fit indices).
That said, it is worth noting that sometimes folks make models unnecessarily complex and then they run into a model that is either just-identified or under-identified. But in these cases, the identification problem comes more from a lack of adequate conceptualization of the relationships involving the variables (resulting in a tendency to specify a model where everything predicts everything - which looks like spaghetti in a diagram!). However, I would point out that you can also have the same problem with spaghetti and still have an over-identified model too. Indeed, you can have an overidentified model that still doesn't say anything useful and/or horribly misspecified! Obviously, in this case, you are able to judge the degree of overall model misspecification using the fit indices.
One final thing: I don't want to give you the impression that model identification is unimportant when judging model fit. You certainly have more information regarding model fit when you have specified an over-identified model as opposed to a just-identified model. My main point is that there may be times when a just-identified model is theoretically logical and defensible and that making tweaks to the model by fixing or removing parameters just to achieve an over-identified model makes no sense.
So there you have it. I appreciate the question because I'm sure that many others have the same question (hell, I had the same question when learning about SEM :) I hope this has made this a little less cloudy!
Best wishes!
Hi Mike, thank you so much for your very detailed answer! In my model, I fixed one of my covariances to 0 as I know that those variables are not correlated, which makes the model over-identified. I guess that works.
At any rate (as you like to say haha), "You can still evaluate the fit of a just-identified model using many of the same indicators you are used to with regression (e.g., significance of path coefficients, R-square values, etc.). [We do that every day using standard OLS regression!]": I haven't look at it this way, but it definitely makes sense :)
Many thanks
If this was a "2-step" path model where age & years predict 2 intermediate variables, which predicts deference...would the variances for these intermediate variables be considered parameters? (assuming no covariance between the two intermediate variables)
In my modell I won't get any numbers because it says it is unidentified. I becomes identified when I give one of the paths from the indicators describing a construct to the construct a regression weight of 1. Is there a way I can get numbers without fixing them? If not, how do I choose the right variable to fix to 1? Thank you!