diff --git a/src/SAS/challenger_SAS_ipynb.ipynb b/src/SAS/challenger_SAS_ipynb.ipynb new file mode 100644 index 0000000000000000000000000000000000000000..41305db13a8dec0a5260d1b0647e3a7e42b1c760 --- /dev/null +++ b/src/SAS/challenger_SAS_ipynb.ipynb @@ -0,0 +1,12703 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "hideCode": true, + "hidePrompt": true + }, + "source": [ + "\n", + "# Risk Analysis of the Space Shuttle: Pre-Challenger Prediction of Failure\n", + "\n", + "*Marie-Gabrielle Dondon*\n", + "\n", + "*11/10/2018*\n", + "\n", + "*This is a SAS version based on the Rmd document of Arnaud Legrand available at [https://app-learninglab.inria.fr](https://applearninglab.inria.fr/gitlab/moocrr-session1/moocrr-reproducibility-study/blob/5e298cd5b653bcb31b6f9fedcb7f75e800c2dc98/src/R/challenger.Rmd) and the SAS program of Michael Friendly available at [https://dokumen.tips](https://dokumen.tips/documents/categorical-data-analysis-with-graphics.html) (cf. page 52).*\n", + "\n", + "---" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "hideCode": true, + "hidePrompt": true + }, + "source": [ + "In this document we reperform some of the analysis provided in \n", + "*Risk Analysis of the Space Shuttle: Pre-Challenger Prediction of Failure* by *Siddhartha R. Dalal, Edward B. Fowlkes, Bruce Hoadley* published in *Journal of the American Statistical Association*, Vol. 84, No. 408 (Dec., 1989), pp. 945-957 and available at http://www.jstor.org/stable/2290069. \n", + "\n", + "On the fourth page of this article, they indicate that the maximum likelihood estimates of the logistic regression using only temperature are: $\\hat{\\alpha}$ = **5.085** and $\\hat{\\beta}$ = **-0.1156** and their asymptotic standard errors are $s_{\\hat{\\alpha}}$ = **3.052** and $s_{\\hat{\\beta}}$ = **0.047**. The Goodness of fit indicated for this model was $G^2$ = **18.086** with **21** degrees of freedom. Our goal is to reproduce the computation behind these values." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "hideCode": true, + "hidePrompt": true + }, + "source": [ + "The DATA step below reads the data on the number of O-ring failures and temperature for the 23 flights forwhich information was available before the Challenger launch. Our interest here is in predicting the likelihood of failures at low temperatures." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "SAS Connection established. Subprocess id is 3488\n", + "\n" + ] + }, + { + "data": { + "text/html": [ + "\r\n", + "\r\n", + "\r\n", + "\r\n", + "\r\n", + "Sortie SAS\r\n", + "\r\n", + "\r\n", + "\r\n", + "

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NASA Space Shuttle O-Ring Failures

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La PRINT Procédure

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Table WORK.NASA

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FlightDateCountTemperaturePressureMalfunction
104/12/81666500
211/12/81670501
303/22/82669500
511/11/82668500
604/04/83667500
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La GPLOT Procédure

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Plot of Freq_Malfunction by Temperature

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Table WORK.NASA2

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FlightDateCountTemperaturePressureMalfunctionFreq_Malfunction
104/12/816665000.00000
211/12/816705010.16667
303/22/826695000.00000
511/11/826685000.00000
604/04/836675000.00000
706/18/826725000.00000
808/30/8367310000.00000
911/28/8367010000.00000
41B02/03/8465720010.16667
41C04/06/8466320010.16667
41D08/30/8467020010.16667
41G10/05/8467820000.00000
51A11/08/8466720000.00000
51C01/24/8565320020.33333
51D04/12/8566720000.00000
51B04/29/8567520000.00000
51G06/17/8567020000.00000
51F07/29/8568120000.00000
51I08/27/8567620000.00000
51J10/03/8567920000.00000
61A10/30/8567520020.33333
61B11/26/8567620000.00000
61C01/12/8665820010.16667
 ..31...
 ..30...
 ..35...
 ..40...
 ..45...
 ..50...
 ..55...
 ..60...
 ..65...
 ..70...
 ..75...
 ..80...
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Sortie SAS

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NASA Space Shuttle O-Ring Failures

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La LOGISTIC Procédure

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Informations sur le modèle

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Informations sur le modèle
TableWORK.NASA2 
Variable de réponse (Evénements)MalfunctionNumber of O-ring failures
Variable de réponse (Expériences)Count 
Modèlelogit binaire 
Technique d'optimisationScore de Fisher 
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Synthèse des observations

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Nb d'observations lues35
Nb d'observations utilisées23
Somme des fréquences lues138
Somme des fréquences utilis138
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Profil de réponse

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Profil de réponse
Valeur
ordonnée		Résultat binaireFréquence
totale
1Evénemen9
2Non-évén129
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Note:12 observations were deleted due to missing values for the response or explanatory variables.

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Etat de convergence

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Etat de convergence du modèle
Critère de convergence (GCONV=1E-8) respecté.
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Qualité de l'ajustement

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Statistique d'adéquation de la déviance et de Pearson
CritèreValeurDDLValeur/DDLPr > Khi-2
Ecart18.0863210.86130.6435
Pearson29.9803211.42760.0924
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Nombre d'observations d'événements/expériences : 23

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Statistiques d'ajustement

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Statistiques d'ajustement du modèle
CritèreConstante uniquementConstante et covariables
Log-vraisemblanceLog-vraisemblance complète
AIC68.54064.39635.647
SC71.46870.25141.501
-2 Log66.54060.39631.647
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Tests globaux

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Test de l'hypothèse nulle globale : BETA=0
TestKhi-2DDLPr > Khi-2
Rapport de vrais6.144010.0132
Score6.769610.0093
Wald6.043510.0140
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Valeurs estimées du paramètre

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Estimations par l'analyse du maximum de vraisemblance
ParamètreDDLEstimationErreur
type		Khi-2
de Wald		Pr > Khi-2
Intercept15.08503.05252.77510.0957
Temperature1-0.11560.04706.04350.0140
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Rapports de cotes

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Estimations des rapports de cotes
EffetValeur estimée du point95% Intervalle de confiance
de Wald
Temperature0.8910.8120.977
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Statistiques d'association

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Association des probabilités prédites et des réponses observées
Pourcentage concordant65.4D de Somers0.382
Pourcentage discordant27.1Gamma0.413
Pourcentage lié7.5Tau-a0.047
Paires1161c0.691
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Sortie SAS

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Odds Ratios

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La PRINT Procédure

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Table WORK.ODDSRATIOS

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EffetEstimation du rapport de cotesBorne inférieure de l'IC à 95% pour le rapport de cotesBorne supérieure de l'IC à 95% pour le rapport de cotes
Temperature0.8910.8120.977
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Sortie SAS

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Parameter Estimates

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Table WORK.PARAMETERESTIMATES

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VariableDDLEstimationErreur typeKhi-2 de WaldPr > Khi-2
Intercept15.084983.052492.77510.0957
Temperature1-0.115600.047026.04350.0140
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Sortie SAS

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Goodness Of Fit

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Table WORK.GOODNESSOFFIT

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CritèreDDLKhi-2Khi-2/DDLPr > Khi-2
Ecart2118.08630.86130.6435
Pearson2129.98031.42760.0924
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Predicted probabilities of a failure

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La PRINT Procédure

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Table WORK.RESULTS

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FlightDateCountTemperaturePressureMalfunctionFreq_Malfunctionpredictlowerupper
104/12/816665000.000000.072780.037160.13767
211/12/816705010.166670.047110.020440.10482
303/22/826695000.000000.052580.024060.11104
511/11/826685000.000000.058640.028090.11837
604/04/836675000.000000.065360.032480.12713
706/18/826725000.000000.037750.014470.09485
808/30/8367310000.000000.033770.012090.09077
911/28/8367010000.000000.047110.020440.10482
41B02/03/8465720010.166670.181790.077030.37163
41C04/06/8466320010.166670.099940.051820.18408
41D08/30/8467020010.166670.047110.020440.10482
41G10/05/8467820000.000000.019230.004680.07557
51A11/08/8466720000.000000.065360.032480.12713
51C01/24/8565320020.333330.260790.090490.55575
51D04/12/8566720000.000000.065360.032480.12713
51B04/29/8567520000.000000.026990.008330.08385
51G06/17/8567020000.000000.047110.020440.10482
51F07/29/8568120000.000000.013670.002590.06887
51I08/27/8567620000.000000.024110.006890.08086
51J10/03/8567920000.000000.017170.003850.07319
61A10/30/8567520020.333330.026990.008330.08385
61B11/26/8567620000.000000.024110.006890.08086
61C01/12/8665820010.166670.165220.073340.33107
 ..31...0.817770.159600.99066
 ..30...0.834370.163070.99238
 ..35...0.738640.146150.97902
 ..40...0.613230.130160.94382
 ..45...0.470760.114870.85910
 ..50...0.332900.099790.69198
 ..55...0.218730.083980.46092
 ..60...0.135740.065380.26070
 ..65...0.080980.042020.15038
 ..70...0.047110.020440.10482
 ..75...0.026990.008330.08385
 ..80...0.015320.003160.07097
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Sortie SAS

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La GPLOT Procédure

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Plot of obs by Temperature

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