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## PowerPoint Slideshow about ' Ordinal Data' - arlais

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### Ordinal Data

Sarah Medland

What about more than 2 categories?

- Very similar
- We create a matrix containing the 1st threshold and the displacements between subsequent matrices
- We then add the 1st threshold and the displacement to obtain the subsequent thresholds

-1

1.2

3

-3

0

Mx Threshold Specification: 3+ Cat.Threshold matrix: T Full 2 2 Free

Twin 1 Twin 2

1st threshold

increment

-1

1.2

3

-3

0

Mx Threshold Specification: 3+ Cat.Threshold matrix: T Full 2 2 Free

Twin 1 Twin 2

1st threshold

increment

MxAlgebraL%*%T

-1

1.2

3

-3

0

Mx Threshold Specification: 3+ Cat.Threshold matrix: T Full 2 2 Free

Twin 1 Twin 2

1st threshold

increment

MxAlgebraL%*%T

2nd threshold

Check the xlsspreadsheet…

Two approaches to the liability threshold model

- Solution?
- Traditional
- Maps data to a standard normal distribution
- Total variance constrained to be 1

- Alternate
- Fixes an alternate parameter
- Binary or Ordinal data fix E
- Ordinal data fix 1st two thresholds (aka invariant threshold approach)

- Estimate the remaining parameters

- Fixes an alternate parameter

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