Cette saison, les représentants du championnat de Ligue 1 sont Lille, Lyon et le PSG. Lyon qualifié d'office grâce à la victoire de Chelsea en finale de Ligue Europa, déjà qualifié via son championnat respectif qui libère une place qualifcative dans le 5ème championnat Européen soit la France. La Ligue 1 alignera donc trois clubs qualifiés pour le tirage de la Champions League 2019.

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> From <@uconnvm.uconn.edu:kent@darwin.eeb.uconn.edu> Wed Jan 7 12:51 GMT 1998 > To: ripley@stats.ox.ac.uk (Prof Brian Ripley) > Cc: s-news@utstat.toronto.edu > Subject: Re: Summary of Robust Regression Algorithms > From: kent@darwin.eeb.uconn.edu (Kent E. Holsinger) > > >>>>> "Brian" == Prof Brian Ripley writes: > > Brian> My best example of this not knowing the literature is the > Brian> Hauck-Donner (1977) phenomenon: a small t-value in a > Brian> logistic regression indicates either an insignificant OR a > Brian> very significant effect, but step.glm assumes the first, > Brian> and I bet few users of glm() stop to think. > > All right I confess. This is a new one for me. Could some one explain > the Hauck-Donner effect to me? I understand that the t-values from > glm() are a Wald approximation and may not be terribly reliable, but I > don't understand how a small t-value could indicate "either an > insignificant OR a very significant effect." > > Thanks for the help. It's finding gems like these that make this group > so extraordinarily valuable.

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There is a little-known phenomenon for binomial GLMs that was pointed out by Hauck & Donner (1977: JASA 72:851-3). The standard errors and t values derive from the Wald approximation to the log-likelihood, obtained by expanding the log-likelihood in a second-order Taylor expansion at the maximum likelihood estimates. If there are some \hat\beta_i which are large, the curvature of the log-likelihood at \hat{\vec{\beta}} can be much less than near \beta_i = 0, and so the Wald approximation underestimates the change in log-likelihood on setting \beta_i = 0. This happens in such a way that as |\hat\beta_i| \to \infty, the t statistic tends to zero. Thus highly significant coefficients according to the likelihood ratio test may have non-significant t ratios.

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