Thank you! Yes, you can strict for strict MI (equal residual/error variances) but this has to be done manually in the current Mplus version. See my video here: ruclips.net/video/DFAq5WT9i9k/видео.html Best, Christian Geiser
Thanks, I was not aware of this very useful analysis option in Mplus. I still work with version 7 were this is probably not available but I know that this kind of analysis options are given in JASP software on the basis of the r-package lavaan.
Thanks for the video. What about when the first part of the output for the configural, metric, and scalar models have significant chi square values but the comparison models (e.g., configural vs metric, metric vs scalar, etc.) do not?
When the less restricted model does not fit according to the chi-square model fit test, strictly speaking, chi-square difference tests relative to other models should not be conducted. For example, when the configural model is rejected according to the chi-square test, it doesn't make a lot of sense to compare it to the metric model (which is even more restricted) using a chi-square difference test . Best, Christian Geiser
Hi Dr. Geiser! Thank you for all these useful videos on SEM! My advisor and I would like to take a closer look at the Mplus defaults of this Multigroup CFA Automated Invariance Testing. Where can I find more information about this? Thank you!
Dr. Geiser, thank you for sharing this very informative video. I have a few quick questions for you after reviewing your materials: 1. Do you need a minimum number of cases per group to do the testing? I read the minimum is 200 cases per group, but I see you have fewer (i.e., 179 in your control group). 2. I want to see if my measure holds across (a) gender, (b) race, (c) intersections of gender and race, and (d) across three survey time points. None of these variables are dichotomous-- as even gender has three levels. Would I need to dichotomize these variables and test one at a time, or could I use a grouping variable with more than two categories? 3. If one's chi-square p-values are significant, I assume that means you do have measure variance. Would you then need to make separate factors for each grouping variable OR try again to make a factor that does not vary by group?
Hi Kaitlyn, Thank you for watching my video! Below are my answers to your questions: 1. The sample size question is difficult to answer in general because it depends on many factors including model structure, effect sizes, and number and quality of the indicators. Simulation is a good way to examine sample size requirements for a specific application. 2. Multigroup analysis is not limited to the case of only two groups. You can use grouping variables with > 2 categories. 3. If you find measurement non-equivalence across groups, that could be an interesting finding in and of itself but it is difficult to say in general. One would have to see your specific case/results. Best, Christian Geiser
Dear Christian, (Sorry for my English) I have seen your video about the function MODEL = CONFIGURAL METRIC SCALAR. It works perfect, thanks. However, it does not work for models with second order factors. Do you recommend any video, book, from where I can see the syntax, to perform a factor invariance analysis, but in the "old" way? That allows to measure the invariance (configural, metric and scalar). Thank you very much for your videos. I have learned a lot. Best regards. Flavio.
Hi Flavio, Thank you for watching! Have you checked out the following document? It appears to be pretty comprehensive with regard to the Mplus specification of multigroup analysis/manual invariance testing: blogs.lse.ac.uk/lcat/files/2015/08/LCAT_Mplus_and_R.pdf Best, Christian Geiser
Lo siento. Thank you Christian. This is valid for ordinal variables and grouping with more of 2 category? For example: GROUPING = G (1 = Chile 2 = Argentina 3 = Alemania);
Hi Flavio, You can definitely use more than two groups in multigroup analysis in Mplus. It appears that you can use MODEL = CONFIGURAL METRIC SCALAR also with ordinal outcome variables, except that METRIC is not available for binary (dichotomous) outcomes. Best, Christian Geiser
Thank you so much for this great video. How would you report the comparison results between the models? Would this be acceptable Δ χ² = 1.215, p = .545 (for metric against configural) ? Thanks ! :)
I would include the degrees of freedom (df) in parentheses behind Δ χ² before the = sign. For example, if the df for the difference test were 4, I would write: Δ χ²(4) = 1.215, p = .545. Best, Christian Geiser
Dear Christian, do you know if automated invariance testing can be done with other indices p.ex CFI ? From the output, only the Chi-Square is available. To your knowledge is there a way to add other indices ? Thanks !
Hi Dr. Gesier or QuantFish reps, What does it mean if the output says I have configural invariance (p < .05), but do not have metric or scalar (each p>.05), or that I just do not have metric (p>.05)?
Hi Kaitlyn, A small p value for a difference test (e.g., p < .05) means the more restrictive (more constrained) model fits worse than the less restrictive model. For example, metric invariance is more constrained (and may fit worse) than configural invariance. When the metric invariance model fits worse than the configural model, this may indicate that some or all of the factor loadings differ across some or all of the groups. Some or all of the items/measures may function differently across groups (indicating at least partial measurement non-equivalence). Best, Christian Geiser
Thank you, Christian. Is it possible I don't have configural because my latent facor only has 3 items? I'm wondering if Mplus can assess configural on such a small latent factor. @@QuantFish
@@KaitlynStormes Hi Kaitlyn, I'm not sure I understand the issue(s) that you are facing. If you don't have configural invariance, then you would not even test metric or scalar invariance. In case you are interested, I do offer personal consulting packages (christiangeiser.com/consulting). Best, Christian Geiser
Hi again, Christian; my apologies for the confusion. I'm new to this, but what I meant to say is that my output suggests I have configural invariance (p < .05) but do not have metric (p > .05) and, in some cases, do not have metric or scalar invariance (both p > .05). I heard that having configural invariance but not the later more strict options might be because of my use of a small, 3-item factor.@@QuantFish
@@KaitlynStormes Hi Kaitlyn, If your model is a single factor model with just three indicators, then the configural model would be saturated (zero degrees of freedom) and would trivially fit the data perfectly. The metric and scalar models would be overidentified (non-saturated) even with just 3 indicators as they include equality constraints on factor loadings and/or intercepts across groups. Hence, only the metric and scalar models could actually be tested against the data in this case. I'm not sure about your p-value interpretation. A small p value (e.g., p < .05) for a chi-square difference test suggests that the more constrained model DOES NOT fit. Best, Christian Geiser
Thank you Christian! It is very helpful! But when I used second-order factors, it happened:*** ERROR in ANALYSIS command Measurement invariance testing with the MODEL option of the ANALYSIS command is not allowed when the model contains second-order factors. MODEL=CONFIGURAL is not allowed for this analysis.
![I.N "HALLUCINATION" | [Stray Kids : SKZ-PLAYER]](http://i.ytimg.com/vi/n5B5q1Hwt_U/mqdefault.jpg)
Fantastic video! Is there a step you can take after this to test for strict/residual invariance?
Thank you! Yes, you can strict for strict MI (equal residual/error variances) but this has to be done manually in the current Mplus version. See my video here:
ruclips.net/video/DFAq5WT9i9k/видео.html
Best, Christian Geiser
Thanks, I was not aware of this very useful analysis option in Mplus. I still work with version 7 were this is probably not available but I know that this kind of analysis options are given in JASP software on the basis of the r-package lavaan.
Hi Gert,
Good to know!
Best, Christian Geiser
Thanks for the video. What about when the first part of the output for the configural, metric, and scalar models have significant chi square values but the comparison models (e.g., configural vs metric, metric vs scalar, etc.) do not?
When the less restricted model does not fit according to the chi-square model fit test, strictly speaking, chi-square difference tests relative to other models should not be conducted. For example, when the configural model is rejected according to the chi-square test, it doesn't make a lot of sense to compare it to the metric model (which is even more restricted) using a chi-square difference test .
Best, Christian Geiser
Hi Dr. Geiser! Thank you for all these useful videos on SEM! My advisor and I would like to take a closer look at the Mplus defaults of this Multigroup CFA Automated Invariance Testing. Where can I find more information about this? Thank you!
See the Mplus User's Guide (statmodel.com/download/usersguide/MplusUserGuideVer_8.pdf), section starting on p. 540.
Best, Christian Geiser
@@QuantFish Thank you very much!
Dr. Geiser, thank you for sharing this very informative video. I have a few quick questions for you after reviewing your materials:
1. Do you need a minimum number of cases per group to do the testing? I read the minimum is 200 cases per group, but I see you have fewer (i.e., 179 in your control group).
2. I want to see if my measure holds across (a) gender, (b) race, (c) intersections of gender and race, and (d) across three survey time points. None of these variables are dichotomous-- as even gender has three levels. Would I need to dichotomize these variables and test one at a time, or could I use a grouping variable with more than two categories?
3. If one's chi-square p-values are significant, I assume that means you do have measure variance. Would you then need to make separate factors for each grouping variable OR try again to make a factor that does not vary by group?
Hi Kaitlyn,
Thank you for watching my video! Below are my answers to your questions:
1. The sample size question is difficult to answer in general because it depends on many factors including model structure, effect sizes, and number and quality of the indicators. Simulation is a good way to examine sample size requirements for a specific application.
2. Multigroup analysis is not limited to the case of only two groups. You can use grouping variables with > 2 categories.
3. If you find measurement non-equivalence across groups, that could be an interesting finding in and of itself but it is difficult to say in general. One would have to see your specific case/results.
Best,
Christian Geiser
Thank you. Your responses were very helpful!@@QuantFish
Dear Christian,
(Sorry for my English)
I have seen your video about the function MODEL = CONFIGURAL METRIC SCALAR. It works perfect, thanks.
However, it does not work for models with second order factors. Do you recommend any video, book, from where I can see the syntax, to perform a factor invariance analysis, but in the "old" way? That allows to measure the invariance (configural, metric and scalar).
Thank you very much for your videos. I have learned a lot.
Best regards.
Flavio.
Hi Flavio, Thank you for watching! Have you checked out the following document? It appears to be pretty comprehensive with regard to the Mplus specification of multigroup analysis/manual invariance testing:
blogs.lse.ac.uk/lcat/files/2015/08/LCAT_Mplus_and_R.pdf
Best, Christian Geiser
Thank you Christian. Is the function of 'Analysis: Model=configural metric scalar' from recent Mplus versions?
Yes, I believe it has been added recently.
@@QuantFish thank you so much! That’s good to know ☺️
Lo siento.
Thank you Christian.
This is valid for ordinal variables and grouping with more of 2 category? For example:
GROUPING = G (1 = Chile 2 = Argentina 3 = Alemania);
Hi Flavio,
You can definitely use more than two groups in multigroup analysis in Mplus. It appears that you can use MODEL = CONFIGURAL METRIC SCALAR also with ordinal outcome variables, except that METRIC is not available for binary (dichotomous) outcomes. Best, Christian Geiser
Thank you so much for this great video. How would you report the comparison results between the models? Would this be acceptable Δ χ² = 1.215, p = .545 (for metric against configural) ? Thanks ! :)
I would include the degrees of freedom (df) in parentheses behind Δ χ² before the = sign. For example, if the df for the difference test were 4, I would write:
Δ χ²(4) = 1.215, p = .545.
Best, Christian Geiser
@@QuantFish Thank you Christian ! You're the best !
Dear Christian, do you know if automated invariance testing can be done with other indices p.ex CFI ? From the output, only the Chi-Square is available. To your knowledge is there a way to add other indices ? Thanks !
@@gabgabgab07 You would probably have to calculate the differences in fit statistics by hand.
Best, Christian Geiser
Hi Dr. Gesier or QuantFish reps,
What does it mean if the output says I have configural invariance (p < .05), but do not have metric or scalar (each p>.05), or that I just do not have metric (p>.05)?
Hi Kaitlyn,
A small p value for a difference test (e.g., p < .05) means the more restrictive (more constrained) model fits worse than the less restrictive model. For example, metric invariance is more constrained (and may fit worse) than configural invariance. When the metric invariance model fits worse than the configural model, this may indicate that some or all of the factor loadings differ across some or all of the groups. Some or all of the items/measures may function differently across groups (indicating at least partial measurement non-equivalence).
Best, Christian Geiser
Thank you, Christian. Is it possible I don't have configural because my latent facor only has 3 items? I'm wondering if Mplus can assess configural on such a small latent factor. @@QuantFish
@@KaitlynStormes Hi Kaitlyn,
I'm not sure I understand the issue(s) that you are facing. If you don't have configural invariance, then you would not even test metric or scalar invariance. In case you are interested, I do offer personal consulting packages (christiangeiser.com/consulting).
Best, Christian Geiser
Hi again, Christian; my apologies for the confusion. I'm new to this, but what I meant to say is that my output suggests I have configural invariance (p < .05) but do not have metric (p > .05) and, in some cases, do not have metric or scalar invariance (both p > .05). I heard that having configural invariance but not the later more strict options might be because of my use of a small, 3-item factor.@@QuantFish
@@KaitlynStormes Hi Kaitlyn, If your model is a single factor model with just three indicators, then the configural model would be saturated (zero degrees of freedom) and would trivially fit the data perfectly. The metric and scalar models would be overidentified (non-saturated) even with just 3 indicators as they include equality constraints on factor loadings and/or intercepts across groups. Hence, only the metric and scalar models could actually be tested against the data in this case.
I'm not sure about your p-value interpretation. A small p value (e.g., p < .05) for a chi-square difference test suggests that the more constrained model DOES NOT fit.
Best, Christian Geiser
Thank you Christian! It is very helpful! But when I used second-order factors, it happened:*** ERROR in ANALYSIS command
Measurement invariance testing with the MODEL option of the ANALYSIS command is
not allowed when the model contains second-order factors. MODEL=CONFIGURAL
is not allowed for this analysis.
How to use the command in second-order factors😭?
Thanks for watching! In a second-order CFA, you may have to test MI by specifying the relevant equality constraints manually. Best, Christian Geiser