Hi all,

I've been reading a book by James Grice about observation oriented modelling (an approach to data analysis where one focuses on single cases rather than variables and aggregates). This article summarises the approach.

Grice suggests an unusual way of analysing data based on Procrustes rotation, with the goal of determining the causes of the behaviour of individuals. In this analysis type, the data describing individuals is always recorded in dichotomous/binary form (i.e., whether or not each person possesses some specific attribute).

For example, imagine we have a group of people who either do or don't have the attributes

Depression Anxiety

0 1

1 0

1 1

We also know each person's gender, and whether they're receiving behavioural therapy or not, and we record this in the "conforming" matrix (the IVs):

BehTherapy Gender

0 0

0 1

1 1

Now, to determine if behavioural therapy and gender cause whether or not these individuals have depression and anxiety, we use a binary Procrustes rotation to rotate the conforming matrix towards the target matrix (with the goal of minimising the sum of squared differences between the target and rotated conforming matrix). This produces a rotated or "conformed" version of the original matrix of IVs.

We then tally up the number of hits - e.g., was the rotation able to predict that participant 1 did not have anxiety, that participant 3 did have anxiety, etc? (IIRC this is done simply by looking at whether each value in the rotated/conformed matrix is closer to 1 or closer to zero, and then comparing this dichotomised prediction to the true value for that cell in the target matrix). You can then count up the overall percentage of correct classifications.

After this, a permutation test is performed to see whether the percentage of correct classifications is greater than one would expect by chance alone.

Grice seems to regard this analysis as something completely different from traditional variable-focused statistical analyses and significance tests. But I look at all this and think to myself that this all seems very similar to perfectly standard analyses.

I'm especially interested whether this process of Procrustes rotation shares any specific similarities with other established statistical methods - I have a hunch that this is actually just a subtype of canonical correlation or multivariate regression. I wondered whether some of you with better mathematical statistics knowledge than me might have some more sophisticated thoughts on the differences between Procrustes rotation and other methods for looking at the relationship between two matrices? Is this just old wine in new jars, or is the technique doing something genuinely novel?

I've been reading a book by James Grice about observation oriented modelling (an approach to data analysis where one focuses on single cases rather than variables and aggregates). This article summarises the approach.

Grice suggests an unusual way of analysing data based on Procrustes rotation, with the goal of determining the causes of the behaviour of individuals. In this analysis type, the data describing individuals is always recorded in dichotomous/binary form (i.e., whether or not each person possesses some specific attribute).

For example, imagine we have a group of people who either do or don't have the attributes

*depression*and*anxiety*, as recorded in the matrix below (the "target" matrix - one which basically shows the DVs):Depression Anxiety

0 1

1 0

1 1

We also know each person's gender, and whether they're receiving behavioural therapy or not, and we record this in the "conforming" matrix (the IVs):

BehTherapy Gender

0 0

0 1

1 1

Now, to determine if behavioural therapy and gender cause whether or not these individuals have depression and anxiety, we use a binary Procrustes rotation to rotate the conforming matrix towards the target matrix (with the goal of minimising the sum of squared differences between the target and rotated conforming matrix). This produces a rotated or "conformed" version of the original matrix of IVs.

We then tally up the number of hits - e.g., was the rotation able to predict that participant 1 did not have anxiety, that participant 3 did have anxiety, etc? (IIRC this is done simply by looking at whether each value in the rotated/conformed matrix is closer to 1 or closer to zero, and then comparing this dichotomised prediction to the true value for that cell in the target matrix). You can then count up the overall percentage of correct classifications.

After this, a permutation test is performed to see whether the percentage of correct classifications is greater than one would expect by chance alone.

Grice seems to regard this analysis as something completely different from traditional variable-focused statistical analyses and significance tests. But I look at all this and think to myself that this all seems very similar to perfectly standard analyses.

I'm especially interested whether this process of Procrustes rotation shares any specific similarities with other established statistical methods - I have a hunch that this is actually just a subtype of canonical correlation or multivariate regression. I wondered whether some of you with better mathematical statistics knowledge than me might have some more sophisticated thoughts on the differences between Procrustes rotation and other methods for looking at the relationship between two matrices? Is this just old wine in new jars, or is the technique doing something genuinely novel?

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