This not taken from an article. This is my template based on my own publishing history. You can cite my book Applied Structural Equation Modeling using AMOS if you need a citation.

With invariance testing, you are constraining the measurement properties to be equal across the groups. You are then examining to see if a significant difference exists. Unconstrained means the two groups are assessed independently and no relationships is constrained to be equal across the groups.

That is based on the work of Kline 2011 (referenced at the end of chapter 4). You will also see some say an "acceptable" fit is anything under 5. CMIN (chi-square) can be biased especially with large samples. Understanding the relative chi-square: chi-square/df will present a more rounded approach.

​@@joelcollier9387 OK, Thanks

Thanks. The data is this video was made up for the book Applied Structural Equation Modeling using AMOS. I needed a clean data set to work with. Saying that, the original research using these variables was published in the Journal of Business Research. The title was: Idiosyncratic service experiences: When customers desire the extraordinary in a service encounter

​@@joelcollier9387 I apologize for any confusion. I would like to cite your method for testing the moderation effect in my paper, so I need a scientific reference for your method. I don't require a reference for the data. Thank you! :)

@@yl3355 You can cite the book but you can also cite Marsh, Herbert W. Zhongline Wen, and Kit-Tai Hau. (2008). "Structural Equation Models of Latent Interaction and Quadratic Effects", in Gregory Hancock and Ralphy D. Mueller (eds) Structural Equation Modeling: A Second Course. Greenwich, CT: Information Age

Much appreciated!!

If the lower bound to upper bound confidence interval does not cross "0", then it is significant at .05 level

@@joelcollier9387 What about the above conditions? Can it be called significant or not?

@@makmursujarwo9458 Yes, since it does not cross zero then it is significant at the .05 level.

Trying to test moderated mediation with higher order constructs (with subdimensions) is extremely difficult. The reason why is you need to form an interaction term with the moderator and the independent variable. The most popular was to handle this is to create composite variables. To your point 2, the book talks about comp_friendly and comp_adapt. This is where the latent variables were created into composite scores for each construct. This is not unique to moderated mediation....it is just the most efficient way to handle a complex problem. Can you test moderated mediation with latent variable? Yes. I have another video on RU-vid called how to test moderation with Unobserved variables that explains how to do this. Hope that helps.

Hello, first of all, thank you very much for your reply. I have improved my analysis by following your suggestions and your book. If you have time, I have a few more questions. 1. For example, considering figure 7.19 in the moderation section of your book, if "Adaptive Behaviour" has 3 sub-factors and "Customer Delight" has 2 sub-factors, will there be a change in the analysis direction of the model? 2. For the Modareted Mediation model, I arranged it as Path Model, Full Indicator Model, Mixed Model in accordance with the instructions in the book. Unlike yours, the Interaction variable gave slightly different results in all 3 techniques. Even the path model was meaningless. Other variables in the model were close to each other. Could the sample have an effect on this? Unfortunately, my sample is limited to 205 due to the subject. There are also 49 variables in the model. 3. When I created the "composite variable" for the path model, unlike yours, the variables had sub-dimensions. I first took the average of the sub-dimensions and then calculated the value of the variable by taking the average of the sub-dimensions. Is the path I followed correct? I am grateful for your contribution in advance.

@@cihanuyank9749 So lets just clean up a little terminology first and that should help things. Adaptive behavior does not have "sub factors" those are the observed indicators or measurement items for the construct. To form a composite variable, one usually takes an average of all the observed variable scores and then you have a single score that represents to the construct. You will most likely have different results if you run this moderated mediation model as a path model and then as a full indicator or mixed model method. The reason why is you are accounting for measurement error in the full indicator and mixed model. You are not accounting for measurement error in the path model. Your sample is a little small for that much analysis and that might have something to do with it. With that small of a sample, I would encourage you to run it as a path model and have all your constructs as composite variables. It will make things easier for you.

yes, you will need to bootstrap the data if it is non-normal. Especially if both groups are non-normal.

You only need to run the bootstrap for the structural model. The CFA should be fine without the bootstrapping. Best of luck with the thesis.

@@joelcollier9387 Thank you Joel! Final question- the p value for the Bollen-Stine bootstrap is non-significant (0.642), but it states that the model fit better in 1788 sample, and worse in 3212 samples. Can it still be claimed that the model fit is adequate with the bootstrap samples?

AMOS can not account for Sample weights. You need to weight the data in SPSS (new data column) and then pull that variable into AMOS. Little bit of a work around

If the measures are formative to an unobservable construct, then you do not have to do an invariance test. Invariance testing is for unobserved constructs with reflective measures

Short answer...no. You can not run a categorical variable with just one value. You will have no variance in the data. If the value is categorical you are going to need to assess at least two categories

There are a lot of reason for an iteration limit....if I am taking my best guess, you have multicollinearity in your model. Look for the two unobserved variables that are highly correlated with one another. You may have so much overlap that AMOS can not get a unique solution

@@joelcollier9387 thank you!

If your survey items are the exact same and you do not believe that your groups are fundamentally different, then you can proceed without doing an invariance test. Saying that, I almost always see reviewers asking for an invariance test in multi-group analysis even if there is no fundamental difference between the groups. I would say go ahead and perform it because it makes your study look all the more rigorous.

@@joelcollier9387 Thanks Prof.

With a two group analysis you are looking for differences in the structural relationships across constructs. You are not looking for differences in the measurement properties of the construct across different groups. If you think managers and salespeople are going to interpret a question differently (even if it is worded similarly) then your differences have more to do with how the construct is measured as opposed to group differences. Thus, you would need to perform a measurement model invariance test.

@@joelcollier9387 Thanks prof. for your kind reply. Please tell should i go for measurement invariance testing(MICOM) of my groups, if i have created them from the same collected data using cluster analysis on 4 of my observed items (assessing attitude). Although all my respondents are tourists, but they differ in their attitude, so later on after clustering, i want to know differences in them on "experience and satisfaction relationship". Shall i do measurement invariance, or how shall i proceed...?

There is a lot of debate around this. If you use PROCESS, it does not even give you model fit statistics. If your model fit is bad in SEM, then it points to a model that is not representing the data. In essence, the model does a poor job explaining the data collected. Saying that, it does not mean it poorly explains certain relationships. It means that the totality of your model does not explain the data very well.

@@joelcollier9387 thank you so much for your response. Please would you recommend any references I can check to dig into this discussion ? I am interested in a certain relationship between two constructs of my structural model. The regression weight is 0.24- which is low, but it exists.However, my CFI is 0,.86, Is there any way I can address how reliable this relationship is since the model doesn't fit?

Sadly, no. AMOS does not run multilevel analysis. Your best bet for multilevel analysis is MPLUS

My best guess is if you are having model fit issues...you most likely have measurement issues with your latent constructs. You might want to find the troublesome items and see if it warrants deletion if it is not contributing to the validity of the construct.

@@joelcollier9387 thank you for your response, I will look at my latent constructs. My data does not follow a normal distribution, some literature suggests to transform the non-normal variables before uploading them to Amos, if necessary (Niels.J , 2013)., would this approach be far different from bootstrapping?

Yes, you are only really concerned with outliers in the variables of your structural model.

I always encourage you to impute data in SPSS/SAS/Excel before starting to analyze the data. It is the easiest way to address missing data. You can do it in AMOS but it is not that easy. Try imputing your missing data and then try it again.

Control variables are trying to account for variance in your model in explaining the dependent variable. Two group analysis is examining if relationships are significantly different across the groups. Control variables are necessary if you think that a variable will change the outcome of your dependent variable....for instance Age and technology acceptance.

Yes, you need to assess model fit before you even start addressing the two group analysis. You will have a model fit statistic for each group that needs to be presented

I assess model fit before adding control variables. Many control variables will have relatively no influence but will cause unexplained variance in the model. In my opinion, assess the model fit with the initial structural model and then add you control variables after that. Is it wrong to assess model fit with the control variables included? No but it will usually produce more unexplained variance which could hurt model fit...especially if the control variables are not significant.

Give me an email address and I'll send it to you. Cheers.

Yes, you can. With one DV the analysis will be exactly the same. PROCESS is quicker to use because of the preformed models. If the preformed models do not line up with your model, you are better off using SEM

Yes, you absolutely can do that. You will just have an interaction term with the mediator and moderator to the DV along with a moderator with a relationship to the DV.

Thanks! What would be the indirect effect of ID on DV? I mean do I need to have a direct effect from ID to the moderator and interaction term as well?@@joelcollier9387

If you are talking about the degrees of freedom calculation, it is : Rigdon, Edward E. (1994), "Calculating Degrees of Freedom for a Structural Equation Model", Structural Equation Modeling, 1 (3), 274-278

No. One of the assumptions of SEM is that the DVs are continuous. You might want to try the PROCESS macro otherwise you will need to do logistic regression to find your answers

OK sir

In the output in the estimates tab, you will see a column called "C.R". That stands for Critical ratio which is also the T-value for that specific relationship you are trying to test. Hope that helps.