# Causality analysis in Amos w/ binary independent variables & non-normal distribution

#### fuchs09

##### New Member
Hello,

I'm new to this forum and would highly appreciate your feedback regarding the following situation. As a side note - my statistical knowledge is unfortunately very limited:

Research situation:

I'm analyzing the causality between credit ratings and company strategy. In essence the question is whether the credit rating of a company assigned by rating agencies has any influence on the strategy the management chooses. In turn, the question is also whether the strategy the corporation is choosing influences the rating agencies in the credit rating assignment process.

Research model:

x1 - binary (indicator for positive rating in t)
x2 - binary (indicator for stable rating in t)
x3 - binary (indicator for negative rating in t)
x4 - continous (strategy in t)
x5 - continous (firm characteristics in t)
x6 - continous (firm characteristics in t)
x7 - continous (firm characteristics in t)
y1 - continous (rating in t+1)
y2 - continous (strategy in t+1)

x1 + x2 + x3 + x4 + x6 + x7= y2
x4 + x5 = y1

n:~10,000

Software using:

SPSS & AMOS 22.0

Complication:

My data is not normally distributed as measured in skewness and kurtosis so that I have to bootstrap my data to generate more reliable standard erros and p-values.

However the AMOS program always returns the following error message when trying to perform the ML-estimation or bootstrapping: "The sample moment matrix is not positive definite. It could fail to be positive definite for any of the following reasons:
1. The sample covariance matrix or correlation matrix contains a data
entry error

2. The observed variables are linearly dependent

3. The sample covariance matrix was computed from incomplete data using
the method pairwise deletion

4. The sample correlation matrix contains correlation coefficients
other than product moment correlations."

The problem seems to come from my 3 binary independent variables as the model worked before I have included them. However these three binary variables are crucial for my theory testing and my google search didn't really help me (with my limited understanding) to solve this problem.

Question:

As I'm not very familar with statistics and AMOS it would be great if anyone can give me a hint how to circumvent that problem and get the model up and running.

Thank you very much in advance for considering my post and giving me any advice.

Best,
Martin