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# Synopsis
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The `grmsem` package is an open-source quantitative genetics tool that supports the modelling of genetic and residual covariance structures in samples of unrelated individuals with genome-wide genotyping information. `grmsem` allows fitting different models describing the underlying multivariate genetic architecture of quantitative traits, as captured by a genetic-relationship-matrix (GRM), using structural equation modelling (SEM) techniques and a maximum likelihood approach. Analogous to twin models, the `grmsem` package includes multiple models, such as a `Cholesky decomposition` model, an `Independent Pathway` model and the `Direct Symmetric` model, but also novel models such as a combined `Independent Pathway / Cholesky` model. A general form of these models can be automatically fitted. The user can adapt each model by changing the pre-fitted parameters. All estimates can be obtained in standardised form. Follow-up analyses include estimations of genetic correlations, bivariate heritabilities and factorial co-heritabilities. `grmsem` replaces the package `gsem`, presented in [@StPourcain2018], because an unrelated package with the same name had been released simultaneously.
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The `grmsem` package is an open-source quantitative genetics tool that supports the modelling of genetic and residual covariance structures in samples of unrelated individuals with genome-wide genotyping information. `grmsem` allows fitting different models describing the underlying multivariate genetic architecture of quantitative traits, as captured by a genetic-relationship-matrix (GRM), using structural equation modelling (SEM) techniques and a maximum likelihood approach. Analogous to twin models, the `grmsem` package includes multiple models, such as a `Cholesky decomposition` model, an `Independent Pathway` model and the `Direct Symmetric` model, but also novel models such as a combined `Independent Pathway / Cholesky` model. A general form of these models can be automatically fitted. The user can adapt each model by changing the pre-fitted parameters. All estimates can be obtained in standardised form. Follow-up analyses include estimations of genetic correlations, bivariate heritabilities and factorial co-heritabilities. `grmsem` replaces the package `gsem`, presented in [1], because an unrelated package with the same name had been released simultaneously.
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The user can select pre-specified model structures, including the models
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... | ... | @@ -36,7 +36,7 @@ The lower triangle GRM elements are generated and saved with the [GCTA](https:// |
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```{r eval = FALSE}
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> G <- grm.input("large.gcta.grm.gz")
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> G[1:3,1:3] #Rekationships among the first three individuals
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> G[1:3,1:3] #Relationships among the first three individuals
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[,1] [,2] [,3]
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[1,] 0.99354762 0.02328514 0.01644197
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[2,] 0.02328514 0.99406837 0.01021175
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... | ... | @@ -70,10 +70,10 @@ An example of a [large data set](https://gitlab.gwdg.de/beate.stpourcain/grmsem_ |
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* [Bivariate heritabilities](Bivariate heritabilities)
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## Comparison of bi-variate GCTA and GRMSEM estimates
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The software [gcta](https://cnsgenomics.com/software/gcta/) [@Yang2011] can be used to estimate bivariate genetic correlations based on variance/covariance estimates for two traits. Transforming the quad-variate simulated data `large` grmsem data above into GCTA format (`large.gcta.grm.gz`,`large.gcta.phe`, `large.gcta.grm.id`), the bivariate model estimates from `GREML` and `grmsem` analyses can be compared, [here shown for traits Y1 and Y2](GCTA GRMSEM comparison).
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The software [gcta](https://cnsgenomics.com/software/gcta/) can be used to estimate bivariate genetic correlations based on variance/covariance estimates for two traits. Transforming the quad-variate simulated data `large` grmsem data above into GCTA format (`large.gcta.grm.gz`,`large.gcta.phe`, `large.gcta.grm.id`), the bivariate model estimates from `GREML` and `grmsem` analyses can be compared, [here shown for traits Y1 and Y2](GCTA GRMSEM comparison).
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# References
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1. St Pourcain, B. et al. Developmental Changes Within the Genetic Architecture of Social Communication Behavior: A Multivariate Study of Genetic Variance in Unrelated Individuals. Biological Psychiatry 83, 598–606 (2018). <doi:10.1016/j.biopsych.2017.09.020>
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2. Shapland, C. Y. et al. The Multivariate Genetic Architecture of Literacy-, Language- and Working Memory-related Abilities as Captured by Genome-wide Variation. bioRxiv 2020.08.14.251199 (2020) doi:10.1101/2020.08.14.251199. <doi:10.1101/2020.08.14.251199>
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2. Shapland, C. Y. et al. The Multivariate Genetic Architecture of Literacy-, Language- and Working Memory-related Abilities as Captured by Genome-wide Variation. bioRxiv 2020.08.14.251199 (2020). <doi:10.1101/2020.08.14.251199>
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