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Title should say PATH ANALYSIS, my brain is becoming fried from all the textbooks and posts I've been reading

Hey everyone. I'm a doctoral candidate finishing up my dissertation and I need to be able to speak intelligently about my analysis. I already carried it all out and it came out mixed, as most dissertation research likely does.

Here's a recap: one exogenous variable, two sets of mediator variables (each set represents a different theoretical framework), and one endogenous variable.

1. I had to check, because of my hypotheses and lit review, that the direct relationship exists, so I ran a model with just the exogenous variable and the endogenous variable. The fit stats, unsurprisingly, are bonkers. However, I wasn't concerned because this was just a base model before I added the other variables. I just need help explaining that this is an acceptable decision (and if it's not, some help with what to do about that). (Base Model 1)
2. Next I ran 2 separate models, one for each of the theoretical frameworks, checking to see which mediators were actually predicting, based on the data. (Base Model 2 and Base Model 3)
3. Next I put all the mediators into one model, terrible fit because of the non-significant mediators (Full Model 1)
4. Removed the mediators and only left the significant ones, fit improves (Full Model 2)
5. Removed one more mediator that did not remain significant in the overall model, fit improves (Full Model 3)
6. Allowed covariance of the last standing mediators, final model (Full Model 4)

With a layman's understanding of path analysis, I get all of this and I've seen other researchers run an analysis similarly. However, I need to be able to speak to the model fit at each stage and explain why it looks weird, why it looks bad, etc.

Specifically, the problem: for the initial base model, chi squared is .001, but non-significant. df =2. CFI = 1, TLI = 1.039, RMSEA = 0. Both the base models are pretty similar. Once I add everything, the fit statistics are more interpretable for me. Added the model fit statistics particulars at the bottom

I'm digging around in statistics text books, articles on the topic, even message boards where similar questions have been posted, but I can't figure out how to explain this in a way that I understand. My layman-terms assumption is that because the initial model is so basic (just an IV, a DV, and a control variable), SEM is throwing weird fit statistics because there's really not much room for changes in the parameters. I can't say that during my defense though, and I need to be able to cite something in my paper. For the two other base models, I have even less of an explanation--I believe it's throwing weird fit statistics because of the insignificant mediators, but wouldn't it just show poor fit? Why are the stats all 'good fit' yet insignificant chi square, instead of showing poor fit?

Any articles or cites you've got would be great, I can do the reading on my own to save you time. Would really really appreciate some layman terms explanations though. TIA

Model                      x2           Df    sig.            CFI               TLI    RMSEA        95% CI        SRMR    c2Δ

LL    UL

Base Model 1a    0.001    2    .999    1.000    1.039    .000    .000    .000    .001

Base Model 2b    3.075    8    .930    1.000    1.013    .000    .000    .018    .013

Base Model 3c    10.114    10    .431    1.000    1.000    .006    .000    .057    .023

Full Model 1d    409.172    28    .000    0.836    0.683    .193    .176    .209    .110

Full Model 2e    54.378    10    .000    0.952    0.905    .110    .082    .139    .051    354.794

Full Model 3f           31.632    7    .000    0.962    0.924    .098    .065    .134    .041    22.746

Full Model 4g    5.074    6    .000    1.000    1.003    .000    .000    .062    .017    26.558

a Base Model: Value Congruence to Engagement

b Base Model with JDR Mediators

c Base Model with SDT Mediators

d Full Model: All Mediators

e Full Model Without Non-Significant Mediators

f Full Model Without Non-Significant Meidators or Autonomy

g Full Model WIthout Non-Significant Mediators or Autonomy, Allowing Competence to Covary with Coaching
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It's not clear to me what your base model 1 is. From your description, I would have expected it to have 0 degrees of freedom.

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