Commit c89ff6e9 authored by Damien Leroux's avatar Damien Leroux
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Commit before 0.2 tag.

parent 3a6d24f3
......@@ -38,7 +38,7 @@ The lineal model engine minimizes the residual sum of squares $RSS=\sum_{i \in \
In order to compare two nested models we will then use F-test, that is a measurement of the this compromise between goodness of fit and degrees of freedom cost. (To be fully honest, when we compare to models for pleiotropic effects the residual errors $\varepsilon_i$ won't be a vector but a matrix, its squared sum over individuals won't be number but a vector, and therefore we must use some kind of log-likelihood ratio, and a $\chi^2$ test with appropriate degree of freedom will do the job.)
Lets now suppose that we have current model, and we wander if some new extended model is better. Let $df_{current}$ (resp. $df_{new}$) be the number of degree of freedom for the current model (resp. the new model). This number of degree of freedom is the number of independent parameters in the fitted model, that is the number of independent values the linear model engine has to choose for $\mu_{c}$, $\xi_{g,h,c}$ and $\kappa_{v}$. The test value in then:
Lets now suppose that we have current model, and we wander if some new extended model is better. Let $df_{current}$ (resp. $df_{new}$) be the number of degree of freedom for the current model (resp. the new model). This number of degree of freedom is the number of independent parameters in the fitted model, that is the number of independent values the linear model engine has to choose for $\mu_{c}$, $\xi_{g,h,c}$ and $\kappa_{v}$. The test value is then:
\begin{equation} \label{eq:F-test}
F(\mathbf{H}_{new},\mathbf{H}_{current})=\frac{ \frac{ RSS_{current} - RSS_{new} }{ df_{new}-df_{current} } }{ \frac{RSS_{new}}{\left\vert{\mathbf{N}}\right\vert-df_{new}} }
\end{equation}
......@@ -68,7 +68,7 @@ In the simplest models, each QTL has its own effect without any interaction. Tha
Possible genotypes are then allele pairs $g=(g_1,g_2) \in \mathbf{P}^2$.
\subsubsection{Additive and connected model}
The simplest possible model is the additive and connected one. Each allele has its own effect without any dominance, nor interaction with genetic background.
The simplest model is the additive and connected one. Each allele has its own effect without any dominance, nor interaction with genetic background.
\begin{equation}
\xi_{g,h,c_i} = \xi_{(g_1,g_2),\set{l},c_i} = \alpha_{g_1,l}+\alpha_{g_2,l}
\end{equation}
......
......@@ -24,6 +24,7 @@
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}
......
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