| Discussion | Similarly, the linear regression structure used to implement the gene-set analysis offers a high degree of extensibility. |
| Discussion | The model is easily generalized to much more general gene-level linear regression models to allow for simultaneous analysis of multiple covariates and gene-sets, opening up a wide range of new testable hypotheses. |
| Gene analysis | This model first projects the SNP matriX for a gene onto its principal components (PC), pruning away PCs with very small eigenval-ues, and then uses those PCs as predictors for the phenotype in the linear regression model. |
| Gene analysis | The linear regression model is also applied when Y is a binary phenotype. |
| Gene-set analysis | As such, using this variable Z a very simple intercept-only linear regression model can now be formulated for each gene set 5 of the form Z5 2 flOT —|— 55, where Z5 is the subvector of Z corresponding to the genes in 5. |
| Gene-set analysis | One complication that arises in this gene-level regression framework is that the standard linear regression model assumes that the error terms have independent normal distributions, i.e. |
| Supporting Information | Gene p-Values were computed using a logistic regression model to compare against the linear regression model used in MAGMA. |
| Supporting Information | Observations are in gray dashed lines With triangles, and black solid lines With circles are the linear regressions . |
| Supporting Information | Observations are in gray dashed lines With triangles, and black solid lines With circles are the linear regressions . |
| Supporting Information | Observations are in gray dashed lines With triangles, and black solid lines With circles are the linear regressions . |
| Supervised learning: Regression | Again, three representative techniques were used to broadly assess the general ability of the data to support predictive models: Lars (regularized linear regression based on Lasso), Gaussian process regression (a nonlinear model), and support vector regression (a ker-nel-based model). |
| Supervised learning: Regression | As a form of linear regression , Lars enables direct inspection of the coefficients contributing to the prediction. |
| Supervised learning: Regression | Lars performs penalized linear regression with the Ll-norm lasso penalty discussed above for PLR. |