# Weird heritability estimates with bivariate sex-lim model using umx

I've been using umx for estimating bivariate sex-lim models (umxSexLim), which been extremely helpful. After estimating the possible models, the scalar model had the best fit to the data.

However, there is one weird result, that I don't seem to understand its source.

For trait X (when testing a bivariate model for X and Y), in the scalar model, the heritability standardised estimates are .04 and .05 for males and females, respectively. However, when estimating the homogeneity model, the joint heritability estimate for males and females is .14 for the same trait X (that is, much higher than both estimates). Furthermore, when testing the scalar model in a univariate analysis just for trait X, the heritability estimates are .12 for males and 0 for females (which make sense according to the MZM(.55)-DZM(.31) and MZF(.09)-DZF(.21) correlations).

Does it make sense that when adding a trait to the analysis, only one estimate would be that different?

I'm trying to figure out if it's a result of "compromises" as part of model estimation, or perhaps there is a technical problem.

I would appreciate your expert's thoughts and opinions.

Thanks,

Noam.

## Check combined correlations

It's unlikely to be a technical issue or optimization problem. Take a look at the rMZ and rDZ for males & females combined. They should jive with the MLEs that you got from modeling. Also, be aware that variance and mean differences can contribute to deviations from rule-of-thumb e.g., 2(rMZ-rDZ) expected MLEs of ACE parameters. Variance differences between MZs and DZs can do have this effect.

I entered a similar response before but it seems to have disappeared, apologies for repost.

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In reply to Check combined correlations by AdminNeale

## Thank you for your response!

The correlations for males and females combined are rMZ: 0.4, rDZ(only same-sex): 0.25, rDZ(with OS): .18 (the OS correlation is .10 [-.04 - .24]). That is, it seems the combined correlations indicate a larger heritability estimate that is not represented in the estimates presented by the scalar model.

The scalar model was selected by fit indices and tests - that is it’s the most parsimonious model that did not affect model fit. However, as the correlation between DZ-OS correlation is almost 0, doesn’t it make more theoretical sense that a qualitative model will be selected? (-2LL: scalar 7060.65, non-scalar 7059.88, AIC: scalar 2542.65, non-scalar 2557.88).

Another thing - according to your comment I checked mean and variance differences between MZ and DZ, and there are significant differences in variances both when looking only on DZ-SS (SD=.57) and on all DZ(SD=.56) (compared to MZ, SD=.64, variable is standardized). What are the implications of these results in how we view are model results?

Thank you so much,

Noam

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