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Ordinal Data. Sarah Medland. What about more than 2 categories?. Very similar We create a matrix containing the 1 st threshold and the displacements between subsequent matrices We then add the 1 st threshold and the displacement to obtain the subsequent thresholds. 2.2. -1. 1.2. 3.

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ordinal data

Ordinal Data

Sarah Medland

what about more than 2 categories
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
mx threshold specification 3 cat

2.2

-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

mx threshold specification 3 cat1

2.2

-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

mx threshold specification 3 cat2

2.2

-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

two approaches to the liability threshold model
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
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