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kjetil b halvorsen ♦
kjetil b halvorsen ♦
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Imagine a standard confirmatory factor analysis with one latent variable, L, causing the observed variables (items) q1, q2 and q3. It is my goal to rank all observations on their estimated scores on the latent variable L. So far this is straight-forward.

Yet in my case, the observed q1 to q3 each are averages. I also have access to the corresponding variances of q1 to q3 for each observation, let's call these v1, v2 and v3.

Since each observation can differ in both their mean and variance for each of the q variables, I believe I should somehow incorporate the v variables into the generation of my latent index that I will use as the basis of the ranking.

What do you think is the best way?

I can think of the following solutions:

  1. Estimate L as before based on variables q1 to q3. Analogously estimate latent variable K based on variables v1 to v3. Then do a OLS such that L = K + e, in order to predict L given K.
  2. Estimate the latent variables S, L and K, whereby L and K are estimated as above, but both are sub-scales of S.

There might be more ways I haven't thought of. Anyway, thanks in advance for your help.

Imagine a standard confirmatory factor analysis with one latent variable, L, causing the observed variables (items) q1, q2 and q3. It is my goal to rank all observations on their estimated scores on the latent variable L. So far this is straight-forward.

Yet in my case, the observed q1 to q3 each are averages. I also have access to the corresponding variances of q1 to q3 for each observation, let's call these v1, v2 and v3.

Since each observation can differ in both their mean and variance for each of the q variables, I believe I should somehow incorporate the v variables into the generation of my latent index that I will use as the basis of the ranking.

What do you think is the best way?

I can think of the following solutions:

  1. Estimate L as before based on variables q1 to q3. Analogously estimate latent variable K based on variables v1 to v3. Then do a OLS such that L = K + e, in order to predict L given K.
  2. Estimate the latent variables S, L and K, whereby L and K are estimated as above, but both are sub-scales of S.

There might be more ways I haven't thought of. Anyway, thanks in advance for your help.

Imagine a standard confirmatory factor analysis with one latent variable, L, causing the observed variables (items) q1, q2 and q3. It is my goal to rank all observations on their estimated scores on the latent variable L. So far this is straight-forward.

Yet in my case, the observed q1 to q3 each are averages. I also have access to the corresponding variances of q1 to q3 for each observation, let's call these v1, v2 and v3.

Since each observation can differ in both their mean and variance for each of the q variables, I believe I should somehow incorporate the v variables into the generation of my latent index that I will use as the basis of the ranking.

What do you think is the best way?

I can think of the following solutions:

  1. Estimate L as before based on variables q1 to q3. Analogously estimate latent variable K based on variables v1 to v3. Then do a OLS such that L = K + e, in order to predict L given K.
  2. Estimate the latent variables S, L and K, whereby L and K are estimated as above, but both are sub-scales of S.

There might be more ways I haven't thought of.

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griischdoffer
griischdoffer
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CFA items are averages: should we account for the variance?

Imagine a standard confirmatory factor analysis with one latent variable, L, causing the observed variables (items) q1, q2 and q3. It is my goal to rank all observations on their estimated scores on the latent variable L. So far this is straight-forward.

Yet in my case, the observed q1 to q3 each are averages. I also have access to the corresponding variances of q1 to q3 for each observation, let's call these v1, v2 and v3.

Since each observation can differ in both their mean and variance for each of the q variables, I believe I should somehow incorporate the v variables into the generation of my latent index that I will use as the basis of the ranking.

What do you think is the best way?

I can think of the following solutions:

  1. Estimate L as before based on variables q1 to q3. Analogously estimate latent variable K based on variables v1 to v3. Then do a OLS such that L = K + e, in order to predict L given K.
  2. Estimate the latent variables S, L and K, whereby L and K are estimated as above, but both are sub-scales of S.

There might be more ways I haven't thought of. Anyway, thanks in advance for your help.