# AMOS: Chi-square = .000 Degrees of freedom = 0 Probability level cannot be computed

#### sf319

##### New Member
Hi all,

I just ran a model and the output was:
Chi-square = .000
Degrees of freedom = 0
Probability level cannot be computed

I read around about it, and I learned that it means that the model is "saturated" (i.e.: 9 moments and 9 parameters), meaning that there is an exact solution that AMOS found and thus I cannot use the goodness of fit test.

HOWEVER....I'm just not sure if this is a GOOD thing or a BAD thing. Should I be trying to adjust my model? Is there a way to increase my sample moments?

THANK YOU!!! I *REALLY* appreciate any help/advice!

Best,
Sarah

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#### spunky

##### Can't make spagetti
Re: AMOS: Chi-square = .000 Degrees of freedom = 0 Probability level cannot be comput

HOWEVER....I'm just not sure if this is a GOOD thing or a BAD thing.
I guess it's a bad thing if you want to use your model to explain something. This is merely AMOS telling you that you used up all the information you had available and that your model trivially reproduces the covariance matrix. There is nothing that a model with 0 degrees of freedom help explain and anyone can come up with an infinite set of models that fit the data equally with 0 degrees of freedom. Which one would you prefer? there really is no way of telling. SEM only shows its explanatory power when you have degrees of freedom available, and the more the better. Why? because you can think of degrees of freedom as the number of ways in which your model can be "wrong". So if you are like "oh wow... there are X number of ways in which my model can go wrong and it *STILL* fits the data... this must mean I have a good explanatory model". In your case it's more like "there are no ways in which my model can go wrong. therefore, it trivially fits the data".

Should I be trying to adjust my model? Is there a way to increase my sample moments?
Delete paths. fix loadings or structural coefficients. remove latent variables, if you have too many. no one really wants to look at a SEM model that has 0 degrees of freedom because it's basically useless. much like a regression equation where you have as many predictors as subjects. your R squared will be 1. does that mean your model fits the data perfectly? no. it's just a statistical artifact of the way in which regression works. the same logic applies to SEM.

#### Dason

Re: AMOS: Chi-square = .000 Degrees of freedom = 0 Probability level cannot be comput

your R squared will be 1. does that mean your model fits the data perfectly? no.
Well... technically yes the model does fit the *data* perfectly.

#### spunky

##### Can't make spagetti
Re: AMOS: Chi-square = .000 Degrees of freedom = 0 Probability level cannot be comput

Well... technically yes the model does fit the *data* perfectly.
well... true, it does statistically but you can't derive any useful conclusions from it, which is what I was trying to get at. you're not obtaining any relevant information of it outside from the fact that you used up all the info that you have available. any OLS multiple regression model that uses as many predictors as observations fits the data perfectly.

#### Dason

Re: AMOS: Chi-square = .000 Degrees of freedom = 0 Probability level cannot be comput

you're not obtaining any relevant information of it outside from the fact that you used up all the info that you have available.
I wouldn't go quite so far as to say that you haven't obtained any relevant information. It's true you can't do any formal inference but you still have estimates of the model parameters. If you assume that the model you've fit is the 'true' model those are unbiased estimates.

And believe it or not there are methods to analyze unreplicated experiments where you do end up with 0 df for the error term. Now should you put all of your faith in those methods? Probably not - but sometimes you have no choice.

I'm guessing the OP isn't in that situation and there is probably something that can be done to do better. I don't work with AMOS so I haven't really read the thread in detail.

#### spunky

##### Can't make spagetti
Re: AMOS: Chi-square = .000 Degrees of freedom = 0 Probability level cannot be comput

I wouldn't go quite so far as to say that you haven't obtained any relevant information. It's true you can't do any formal inference but you still have estimates of the model parameters. If you assume that the model you've fit is the 'true' model those are unbiased estimates.
I guess I never thought about it from that perspective. but you are, indeed, correct. you do get the parameter estimates from it. i guess my criticism of saturated models comes more out of tradition my discipline rather than formal statistical theory in which if you end up with a model where you cannot provide a certain degree of uncertainty, then that is a model people don't want to talk about. (yes, we worship the p-value like a god but that's a whole other story). but thank you for pointing that out. it's important to keep it in mind.

And believe it or not there are methods to analyze unreplicated experiments where you do end up with 0 df for the error term. Now should you put all of your faith in those methods? Probably not - but sometimes you have no choice.
I have heard about those, but haven't used them much. Partial Least Squares (PLS) is the only one I've relied on when p>n (for p=predictors and n=observations). we got a dirty looks from the reviewers and had to drop it. nevertheless, I believe people in genetics run into this problem a lot more often than we do which is why you're probably more familiar with them than I am (you used to analyze DNA data and stuff like that, am I correct?)

I'm guessing the OP isn't in that situation and there is probably something that can be done to do better. I don't work with AMOS so I haven't really read the thread in detail.
she is. one of the cardinal sins in SEM is to run out of df's and must be avoided at all costs... at the expense of being shunned by editors in journals, LoLz.

#### sf319

##### New Member
Re: AMOS: Chi-square = .000 Degrees of freedom = 0 Probability level cannot be comput

you guys are AWESOME! Thank you!

#### Dason

Re: AMOS: Chi-square = .000 Degrees of freedom = 0 Probability level cannot be comput

nevertheless, I believe people in genetics run into this problem a lot more often than we do which is why you're probably more familiar with them than I am (you used to analyze DNA data and stuff like that, am I correct?)
I still do work with RNA-seq experiments. But no that's not where I've dealt with it. Even though we don't get *a lot* of replication the datasets I've worked with have all been replicated. For the most part in the field I work in you need q-values of some sort at the end of the day (which are a function of the set of p-values) so replication is a must.

#### noetsi

##### No cake for spunky
Re: AMOS: Chi-square = .000 Degrees of freedom = 0 Probability level cannot be comput

"Perfect" explanatory value generally only occurs when you have no degrees of freedom in practice. Formally this is called "just identified" but I would agree with spunky that you have gained little of substance in doing so (it is an artificial result of having no df). There is no way, at least in social science, to know if you have specified your model perfectly (I doubt that there are any perfect models in social sciences or that in any case you will find one given our present knoweldge level).

I would do something to free up df (there are always ways you can respecify your model to do so).

#### sf319

##### New Member
Re: AMOS: Chi-square = .000 Degrees of freedom = 0 Probability level cannot be comput

So...two more questions:

1) I have attached here a screenshot of my model...you can see there are not too many parameters. I am trying to test to see if Emotional Models of Attachment (measured by early relationships) affect level addiction (measured in the survey).

I'm not sure how I can cut down parameters without losing the whole meaning. For example, I can cut out the latent variable, and just look at the data as a path analysis from the early relationship measures to Addiction, but that would eliminate the theory that Attachment Models are involved, right?

2) Also, in researching more about constraining, I read that I can set the regression (number by the arrow) at 1. But in my case, this would sort of ruin the whole point of running my model, correct?

Sorry if these are stupid questions...I'm just new to all this. THANK YOU SO MUCH for taking the time to answer! I wish I could buy you all a beer!

#### noetsi

##### No cake for spunky
Re: AMOS: Chi-square = .000 Degrees of freedom = 0 Probability level cannot be comput

Unfortunately sometimes you have to chose what to sacrifice. Given that a just identified model is commonly of little value you have to decide what is most important.

I believe, it has been several years since I last did SEM, that you can restrict the variance of certain indicators.

#### spunky

##### Can't make spagetti
Re: AMOS: Chi-square = .000 Degrees of freedom = 0 Probability level cannot be comput

well, couple of things...

(a) the screencap is a little too small to actually make sense of how your model looks like

(b) i agree with noetsi. something's gonna have to go and that something should (hopefully) be guided by some sort of theory or informed decision from you. maybe you have some very reliable items in one of those surveys and you can fix their variances to the observed variance... or maybe you can parcel items so you don't have as many paths... or maybe you should just do away with all the latent variables....

choices, choices... oh so many choices..

#### Lazar

##### Phineas Packard
Re: AMOS: Chi-square = .000 Degrees of freedom = 0 Probability level cannot be comput

As you only have to indicators for your latent, one approach could be to assume equivalence and constrain the loadings to be equal. I do not really see much benefit in this but it is the only viable constraint I see in the model.