"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"%matplotlib inline\n",
"pd.set_option('mode.chained_assignment',None) # this removes a useless warning from pandas\n",
"import matplotlib.pyplot as plt\n",
"\n",
"data[\"Frequency\"]=data.Malfunction/data.Count\n",
"data.plot(x=\"Temperature\",y=\"Frequency\",kind=\"scatter\",ylim=[0,1])\n",
"plt.grid(True)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Logistic regression\n",
"\n",
"Let's assume O-rings independently fail with the same probability which solely depends on temperature. A logistic regression should allow us to estimate the influence of temperature."
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/home/aschmide/miniconda3/lib/python3.7/site-packages/ipykernel_launcher.py:7: DeprecationWarning: Calling Family(..) with a link class as argument is deprecated.\n",
"Use an instance of a link class instead.\n",
" import sys\n"
]
},
{
"data": {
"text/html": [
"
\n",
"
Generalized Linear Model Regression Results
\n",
"
\n",
"
Dep. Variable:
Frequency
No. Observations:
23
\n",
"
\n",
"
\n",
"
Model:
GLM
Df Residuals:
21
\n",
"
\n",
"
\n",
"
Model Family:
Binomial
Df Model:
1
\n",
"
\n",
"
\n",
"
Link Function:
logit
Scale:
1.0000
\n",
"
\n",
"
\n",
"
Method:
IRLS
Log-Likelihood:
-3.9210
\n",
"
\n",
"
\n",
"
Date:
Wed, 15 Apr 2020
Deviance:
3.0144
\n",
"
\n",
"
\n",
"
Time:
15:47:34
Pearson chi2:
5.00
\n",
"
\n",
"
\n",
"
No. Iterations:
6
\n",
"
\n",
"
\n",
"
Covariance Type:
nonrobust
\n",
"
\n",
"
\n",
"
\n",
"
\n",
"
coef
std err
z
P>|z|
[0.025
0.975]
\n",
"
\n",
"
\n",
"
Intercept
5.0850
7.477
0.680
0.496
-9.570
19.740
\n",
"
\n",
"
\n",
"
Temperature
-0.1156
0.115
-1.004
0.316
-0.341
0.110
\n",
"
\n",
"
"
],
"text/plain": [
"\n",
"\"\"\"\n",
" Generalized Linear Model Regression Results \n",
"==============================================================================\n",
"Dep. Variable: Frequency No. Observations: 23\n",
"Model: GLM Df Residuals: 21\n",
"Model Family: Binomial Df Model: 1\n",
"Link Function: logit Scale: 1.0000\n",
"Method: IRLS Log-Likelihood: -3.9210\n",
"Date: Wed, 15 Apr 2020 Deviance: 3.0144\n",
"Time: 15:47:34 Pearson chi2: 5.00\n",
"No. Iterations: 6 \n",
"Covariance Type: nonrobust \n",
"===============================================================================\n",
" coef std err z P>|z| [0.025 0.975]\n",
"-------------------------------------------------------------------------------\n",
"Intercept 5.0850 7.477 0.680 0.496 -9.570 19.740\n",
"Temperature -0.1156 0.115 -1.004 0.316 -0.341 0.110\n",
"===============================================================================\n",
"\"\"\""
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"import statsmodels.api as sm\n",
"\n",
"data[\"Success\"]=data.Count-data.Malfunction\n",
"data[\"Intercept\"]=1\n",
"\n",
"logmodel=sm.GLM(data['Frequency'], data[['Intercept','Temperature']], \n",
" family=sm.families.Binomial(sm.families.links.logit)).fit()\n",
"\n",
"logmodel.summary()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The maximum likelyhood estimator of the intercept and of Temperature are thus $\\hat{\\alpha}=5.0849$ and $\\hat{\\beta}=-0.1156$. This **corresponds** to the values from the article of Dalal *et al.* The standard errors are $s_{\\hat{\\alpha}} = 7.477$ and $s_{\\hat{\\beta}} = 0.115$, which is **different** from the $3.052$ and $0.04702$ reported by Dallal *et al.* The deviance is $3.01444$ with 21 degrees of freedom. I cannot find any value similar to the Goodness of fit ($G^2=18.086$) reported by Dalal *et al.* There seems to be something wrong. Oh I know, I haven't indicated that my observations are actually the result of 6 observations for each rocket launch. Let's indicate these weights (since the weights are always the same throughout all experiments, it does not change the estimates of the fit but it does influence the variance estimates)."
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/home/aschmide/miniconda3/lib/python3.7/site-packages/ipykernel_launcher.py:2: DeprecationWarning: Calling Family(..) with a link class as argument is deprecated.\n",
"Use an instance of a link class instead.\n",
" \n"
]
},
{
"data": {
"text/html": [
"
\n",
"
Generalized Linear Model Regression Results
\n",
"
\n",
"
Dep. Variable:
Frequency
No. Observations:
23
\n",
"
\n",
"
\n",
"
Model:
GLM
Df Residuals:
21
\n",
"
\n",
"
\n",
"
Model Family:
Binomial
Df Model:
1
\n",
"
\n",
"
\n",
"
Link Function:
logit
Scale:
1.0000
\n",
"
\n",
"
\n",
"
Method:
IRLS
Log-Likelihood:
-23.526
\n",
"
\n",
"
\n",
"
Date:
Wed, 15 Apr 2020
Deviance:
18.086
\n",
"
\n",
"
\n",
"
Time:
15:47:34
Pearson chi2:
30.0
\n",
"
\n",
"
\n",
"
No. Iterations:
6
\n",
"
\n",
"
\n",
"
Covariance Type:
nonrobust
\n",
"
\n",
"
\n",
"
\n",
"
\n",
"
coef
std err
z
P>|z|
[0.025
0.975]
\n",
"
\n",
"
\n",
"
Intercept
5.0850
3.052
1.666
0.096
-0.898
11.068
\n",
"
\n",
"
\n",
"
Temperature
-0.1156
0.047
-2.458
0.014
-0.208
-0.023
\n",
"
\n",
"
"
],
"text/plain": [
"\n",
"\"\"\"\n",
" Generalized Linear Model Regression Results \n",
"==============================================================================\n",
"Dep. Variable: Frequency No. Observations: 23\n",
"Model: GLM Df Residuals: 21\n",
"Model Family: Binomial Df Model: 1\n",
"Link Function: logit Scale: 1.0000\n",
"Method: IRLS Log-Likelihood: -23.526\n",
"Date: Wed, 15 Apr 2020 Deviance: 18.086\n",
"Time: 15:47:34 Pearson chi2: 30.0\n",
"No. Iterations: 6 \n",
"Covariance Type: nonrobust \n",
"===============================================================================\n",
" coef std err z P>|z| [0.025 0.975]\n",
"-------------------------------------------------------------------------------\n",
"Intercept 5.0850 3.052 1.666 0.096 -0.898 11.068\n",
"Temperature -0.1156 0.047 -2.458 0.014 -0.208 -0.023\n",
"===============================================================================\n",
"\"\"\""
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"logmodel=sm.GLM(data['Frequency'], data[['Intercept','Temperature']], \n",
" family=sm.families.Binomial(sm.families.links.logit),\n",
" var_weights=data['Count']).fit()\n",
"\n",
"logmodel.summary()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Good, now I have recovered the asymptotic standard errors $s_{\\hat{\\alpha}}=3.052$ and $s_{\\hat{\\beta}}=0.047$.\n",
"The Goodness of fit (Deviance) indicated for this model is $G^2=18.086$ with 21 degrees of freedom (Df Residuals).\n",
"\n",
"**I have therefore managed to fully replicate the results of the Dalal *et al.* article**."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Predicting failure probability\n",
"The temperature when launching the shuttle was 31°F. Let's try to estimate the failure probability for such temperature using our model.:"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"%matplotlib inline\n",
"data_pred = pd.DataFrame({'Temperature': np.linspace(start=30, stop=90, num=121), 'Intercept': 1})\n",
"data_pred['Frequency'] = logmodel.predict(data_pred)\n",
"data_pred.plot(x=\"Temperature\",y=\"Frequency\",kind=\"line\",ylim=[0,1])\n",
"plt.scatter(x=data[\"Temperature\"],y=data[\"Frequency\"])\n",
"plt.grid(True)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The predictiction is not correct. Let's see what went wrong"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"data_pred.plot(x=\"Temperature\",y=\"Frequency\",kind=\"line\",ylim=[0,1.2])\n",
"plt.scatter(x=data[\"Temperature\"],y=data[\"Frequency\"])\n",
"plt.grid(True)"
]
},
{
"cell_type": "markdown",
"metadata": {
"hideCode": false,
"hidePrompt": false,
"scrolled": true
},
"source": [
"This figure is very similar to the Figure 4 of Dalal *et al.* **I have managed to replicate the Figure 4 of the Dalal *et al.* article.**"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Computing and plotting uncertainty"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Following the documentation of [Seaborn](https://seaborn.pydata.org/generated/seaborn.regplot.html), I use regplot."
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"sns.set(color_codes=True)\n",
"plt.xlim(30,90)\n",
"plt.ylim(0,1)\n",
"sns.regplot(x='Temperature', y='Frequency', data=data, logistic=True)\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**I think I have managed to correctly compute and plot the uncertainty of my prediction.** Although the shaded area seems very similar to [the one obtained by with R](https://app-learninglab.inria.fr/moocrr/gitlab/moocrr-session3/moocrr-reproducibility-study/tree/master/challenger.pdf), I can spot a few differences (e.g., the blue point for temperature 63 is outside)... Could this be a numerical error ? Or a difference in the statistical method ? It is not clear which one is \"right\"."
]
}
],
"metadata": {
"celltoolbar": "Hide code",
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.7.6"
},
"toc": {
"base_numbering": 1,
"nav_menu": {},
"number_sections": true,
"sideBar": true,
"skip_h1_title": false,
"title_cell": "Table of Contents",
"title_sidebar": "Contents",
"toc_cell": false,
"toc_position": {},
"toc_section_display": true,
"toc_window_display": false
}
},
"nbformat": 4,
"nbformat_minor": 2
}