Re: Real Hide Ip V4.0.9.2 Portable
Anastacia Iacono
This use-case employs the Poisson distribution for modeling countdata along predicted probabilities for the number of goals in soccermatches from the 2018 FIFA World Cup. The full analysis with anillustrative introduction from basic probability theory to regressionmodels using the R package distributions3is given here.
To investigate the number of goals scored per match in the 2018 FIFAWorld Cup, the FIFA2018 data set provides two rows, one foreach team, for each of the 64 matches during the tournament. In thefollowing, we treat the goals scored by the two teams in the same matchas independent which is a realistic assumption for this particular dataset. We just remark briefly that there are also bivariategeneralizations of the Poisson distribution that would allow forcorrelated observations but which are not considered here.
In addition to the goals, the data set provides some basicmeta-information for the matches (an ID, team name abbreviations, typeof match, group vs. knockout stage) as well as some further covariatesthat we will revisit later in this document. The data looks likethis:
This confirms that goals are relatively rare events in a soccer gamewith each team scoring zero to two goals per match in almost 90 percentof the matches. Below we show that this observed frequency distributioncan be approximated very well by a Poisson distribution which cansubsequently be used to obtain predicted probabilities for the goalsscored in a match.
In a first step, we simply assume that goals are scored with aconstant mean over all teams and fit a single Poisson distribution forthe number of goals. To do so, we obtain a point estimate of the Poissonparameter by using the empirical mean \(\hat\lambda = \bar y = 1.297\) and set up the correspondingdistribution object:
This actually corresponds to the maximum likelihood estimator forthis distribution fitting a generalized linear model (GLM) to the datathat links the expected number of goals per team/match \(\lambda_i\) to the linear predictor \(x_i^\top \beta\) with regressor vector\(x_i^\top\) and correspondingcoefficient vector \(\beta\) using alog-link: \(\log(\lambda_i) = x_i^\top\beta\).
Here, in the simplest case fitting an intercept-only model withoutfurther regressors, the regressor vector can be written as \(x_i^\top = 1\) and the maximum likelihoodestimator \(\hat \beta\) withcorresponding inference, predictions, residuals, etc. can be obtainedusing the glm() function from base R withfamily = poisson:
Or equivalently the predict() function can be used withtype = "response" in order to get the expected \(\hat \lambda_i\) (rather than just thelinear predictor \(x_i^\top \hat\beta\) that is predicted by default).
To account for different expected performances from the teams in the2018 FIFA World Cup, the FIFA2018 data provides anestimated logability for each team. These have beenestimated by Zeileis, Leitner, and Hornik(2018) prior to the start of the tournament (2018-05-20) based onquoted odds from 26 online bookmakers using the bookmaker consensusmodel of Leitner, Zeileis, and Hornik(2010). The difference in logabilitybetween a team and its opponent is a useful predictor for the number ofgoals scored.
Here, the slope of \(0.413\) can beinterpreted as an ability elasticity of the number of goals scored. Thisis because the difference of the log-abilities can also be understood asthe log of the ability ratio. Thus, when the ability ratio increases by\(1\) percent, the expected number ofgoals increases approximately by \(0.413\) percent.
In comparison to the intercept-only model m_ic, thisyields a more realistic outcome providing a different predicted Poissondistribution for each team/match in the tournament. We can set up thevector of all \(128\)Poisson() distribution objects by extracting the vector ofall fitted point estimates \((\hat \lambda_1,\dots, \hat \lambda_128)^\top\):
Marginal calibration is generally concerned with whether the observedfrequencies match the frequencies expected by the model. For discreteobservations, frequencies for the observations themselves can beconsidered; for continuous observations or more generally, frequenciesfor intervals of observations are being used. Here, the expectedfrequencies are computed by differences between the predictive CDFs\(F( \cdot )\), evaluated at theinterval breaks. Hence, marginal calibration is always obtained on theobservation scale compared to the probabilistic calibration performed onthe probability scale. This makes it especially useful for evaluatingcount data models which predictions are often close to zero.
For evaluating the marginal calibration of the Poisson models for thenumber of goals scored, we compute the expected absolutefrequencies by averaging across the expectations per team/match fromboth regression model and compare these with the observed absolutefrequencies:
Graphically, this comparison can be shown as a so-calledrootogram (Kleiber and Zeileis2016) where the gray bars represent the observed frequenciesoverlayed by the expected frequencies as a red line. By using thefunction rootogram(), we can reproduce the previous resultsplugging in the model objects m_ic andm_reg:
So far we have only evaluated the marginal calibration comparingwhether the observed frequencies match the frequencies expected byestimated model on the observational scale. In the next step we willevaluate the probabilistic calibration which is performed on theprobability scale.
To focus more on violations of the distributional assumption in thetails of the distribution, PIT residuals can also be transformed to thenormal scale or another scale if preferred. This allows the extremevalues to be spread more widely, so that less values are included in theouter intervals. However, this has the drawback that detectingmisspecification is more complicated than checking for uniformity:
Discretization, i.e., the representation of values in intervals, hasthe advantage that it usually improves the readability of graphicalrepresentations. However, discretization can also hide certainmisspecifications: breakpoints are often quite arbitrary and can maskmisspecifications of relatively few but extreme values in the outertails of the distribution. Here, classical Q-Q plots areclearly superior to PIT histograms:
Since small to medium deviations are nevertheless difficult to detectin Q-Q plots, untilting the plot makes detecting pattern ofdeparture from a now horizontal line much easier. Here, expectedquantiles are subtracted from the observed quantiles:
As you have probably noticed, we're also bringing completely new documentation pages built on top of Blazorise. When Blazorise was first created almost four years ago, Blazor was limited to very basic features. There was no server-side, no way to do the proper SEO, etc. And so, the only way to do the proper documentation at the time was to use GitHub pages. As time went by, with all the work on new features, documentation was always last to go. But this time Blazorise's documentation is built from the ground up, completely with Blazor and Blazorise. We now support real code examples, copy/paste snippets, hide/show code. Many new examples are included and with time we will include even more of them. We hope you will enjoy using the new docs as much as we enjoyed creating them.
No big release can be done without some breaking changes and this release is no exception. Considering this is the last 0.9.* release before 1.0, there was no other time. We tried to make the changes to a minimum but nevertheless, you will need to adjust your code. Here are the required steps that needs to be done:
4. We've found that on Dropdown we had both a VisibleChanged and Toggled event, which served the same purpose. We've removed Toggled and changed VisibleChanged to a regular Blazor EventCallback. Replace any Toggled Parameter with the VisibleChanged Parameter. Change any VisibleChanged event you might've bound to be compliant with a regular Blazor EventCallback.
5. While not strictly a breaking changes, it is advised to also rename all Left and Right values, eg. for TextAlignment and Direction. We have marked them as obsolete and they will be replaced with Start and End values. The purpose of the new values is the better naming support for the RTL support that should take place in the next Blazorise version.
6. We've changed the DataGrid's RowSelectable evaluation to take in a RowSelectableEventArgs instead. This way we can provide you with increased information on the selection being handled. This new RowSelectableEventArgs will still give you access to the current row item and additionaly to the type of selection being done, RowClick, MultiSelectClick, MultiSelectAll You will need to change your RowSelectable handlers to expect a RowSelectableEventArgs instead.
First and foremost, with this release, we finally introduce a new Bootstrap 5 provider. The new Bootstrap 5 is already put to a test and is now running our new documentation pages. You can also see it in our demos.
Now that the .NET 6 is out it is only natural that we want to support it. The old .NET 5 is still supported just in case there are projects that cannot upgrade at this time. Please note, we plan to drop support for .NET 5 once the Blazorise 1.0 is released sometime at the beginning of 2022. Considering that .NET 6 is going to be LTS and that it supports many new features it is the only way to move forward without .NET 5 holding us back.
We have refactored major parts of Blazorise internals to make use of JavaScript modules. As a result of all the hard work, we have made it easier to set up Blazorise projects, and manually importing Javascript static files is not needed anymore. All Blazorise static files can safely be removed from all your index.html and _Layout.cshtml / _Host.cshtml files.
Autocomplete now has support for multiple selection by setting the new Multiple parameter to true. You have two extra Parameters at your disposal to handle the multiple values. SelectedValues and SelectedTexts
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