Aula 4 Objetivos

  • Saber como a realizar regressões em nosso 'pipeline' de trabalho
  • Incentivar o uso de 'predicted values' ao lado de coefficients e p-values

Revisão de Regressões

Regressão é apenas a análise de variação nos dados

Três elementos fundamentais:

  1. A lógica de inferência causal informa quais variáveis incluímos

  2. O tipo/escala da outcome variável informa qual modelo (função de link) usamos

  3. O tipo/escala do tratamento e do resultado determinam como interpretamos os resultados

Fórmula de Regressão

  • Y ~ X
  • Y ~ X1 + X2
  • Y ~ X1*X2

Modelos de Regressão

  • Continuous -> Ordinary Least Squares
    d %>% zelig(Y ~ X,data=.,model="ls")

  • Binary -> Logit
    d %>% zelig(Y ~ X,data=.,model="logit")

  • Unordered categories -> Multinomial logit
    d %>% zelig(Y ~ X,data=.,model="mlogit")

  • Ordered categories -> Ordered logit
    d %>% zelig(Y ~ X,data=.,model="ologit")

  • Count -> Poisson
    d %>% zelig(Y ~ X,data=.,model="poisson")

Interpretação de Regressão

  • Difícil! Depende da escala da variável de tratamento, da escala do resultado, do modelo utilizado e da presença de quaisquer interações, etc.
  • Para o OLS básico: 1 [unidade de tratamento] mudança no tratamento está associada com uma mudança de \(\beta\) [unidades de resultado] no resultado
  • Freqüentemente, é melhor focar nos 'predicted values': Da nossa equação de regressão (com nossos coeficientes estimados), quais valores de \(Y\) esperamos para valores específicos de \(X\)?
    • Ideal para visualização

Usando Zelig

  • Controlando para os horários de partida programados, os diferentes aeroportos têm atrasos médios de partida diferentes?
flights %>% zelig(dep_delay ~ origin + dep_time, data=., model="ls")
## Model: 
## 
## Call:
## z5$zelig(formula = formula, data = data, by = by)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
##  -68.91  -18.61   -8.10    1.36 1305.19 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.365e+01  2.174e-01  -62.81   <2e-16
## originJFK   -4.327e+00  1.631e-01  -26.53   <2e-16
## originLGA   -4.190e+00  1.661e-01  -25.22   <2e-16
## dep_time     2.152e-02  1.389e-04  154.89   <2e-16
## 
## Residual standard error: 38.77 on 328517 degrees of freedom
##   (8255 observations deleted due to missingness)
## Multiple R-squared:  0.0703, Adjusted R-squared:  0.07029 
## F-statistic:  8281 on 3 and 328517 DF,  p-value: < 2.2e-16
## 
## Next step: Use 'setx' method

Tabelas de Regressão

  • Controlando para os horários de partida programados, os diferentes aeroportos têm atrasos médios de partida diferentes?
  • Use stargazer()
  • Lembre-se de definir os parâmetros do chunk como`r, results='asis'`
flights %>% zelig(dep_delay ~ origin + dep_time, data=., model="ls") %>% 
  from_zelig_model() %>%
  stargazer()
Dependent variable:
dep_delay
originJFK -4.327***
(0.163)
originLGA -4.190***
(0.166)
dep_time 0.022***
(0.0001)
Constant -13.655***
(0.217)
Observations 328,521
R2 0.070
Adjusted R2 0.070
Residual Std. Error 38.771 (df = 328517)
F Statistic 8,280.601*** (df = 3; 328517)
Note: p<0.1; p<0.05; p<0.01

Tabelas de Regressão

  • Controlando para os horários de partida programados, os diferentes aeroportos têm atrasos médios de partida diferentes?
  • Use stargazer()
  • Lembre-se de definir os parâmetros do chunk como`r, results='asis'`
flights %>% zelig(dep_delay ~ origin + dep_time, data=., model="ls") %>% 
  from_zelig_model() %>%
  stargazer(title="Regression Results",style="apsr",dep.var.labels=c("Departure Delay"), digits=1)
Regression Results
Departure Delay
originJFK -4.3***
(0.2)
originLGA -4.2***
(0.2)
dep_time 0.02***
(0.000)
Constant -13.7***
(0.2)
N 328,521
R2 0.1
Adjusted R2 0.1
Residual Std. Error 38.8 (df = 328517)
F Statistic 8,280.6*** (df = 3; 328517)
p < .1; p < .05; p < .01

Modelo Logit

  • Controlando para os horários de partida programados, os diferentes aeroportos têm mais ou menos voos partindo na hora?
flights %>% mutate(Late=ifelse(dep_delay>0,1,0)) %>% 
  zelig(Late ~ origin + dep_time, data=., model="logit") %>% 
  from_zelig_model() %>%
  stargazer()
Dependent variable:
Late
originJFK -0.372***
(0.009)
originLGA -0.496***
(0.009)
dep_time 0.001***
(0.00001)
Constant -1.913***
(0.013)
Observations 328,521
Log Likelihood -204,876.000
Akaike Inf. Crit. 409,759.900
Note: p<0.1; p<0.05; p<0.01

Standard Errors

  • Zelig usa automaticamente bootstrapping para calcular standard errors
  • Então eles provavelmente já são SEs "robustos"
  • Infelizmente, não existe uma maneira de especificar SEs em cluster no momento

Predicted values

  • Por exemplo, qual é o atraso médio para um voo das 18h de Newark?
  • Note que quaisquer variáveis que não sejam 'setx' serão definidas para a ** mediana **
flights %>% mutate(origin=as.factor(origin)) %>% 
  zelig(dep_delay ~ origin + dep_time, data=., model="ls") %>% 
  setx(origin="EWR", dep_time=1800) %>%
  sim()
## 
##  sim x :
##  -----
## ev
##       mean        sd      50%     2.5%    97.5%
## 1 25.07474 0.1271728 25.07832 24.82485 25.32464
## pv
##          mean       sd      50%      2.5%    97.5%
## [1,] 25.73726 37.79083 25.56112 -46.07202 103.2223

Predicted values

  • Por exemplo, qual é o atraso médio para um voo das 18h de Newark?
  • Note que quaisquer variáveis que não sejam 'setx' serão definidas para a ** mediana **
flights %>% mutate(origin=as.factor(origin)) %>% 
  zelig(dep_delay ~ origin + dep_time, data=., model="ls") %>% 
  setx(origin="EWR", dep_time=1800) %>%
  sim() %>%
  zelig_qi_to_df()
setx_value dep_time origin expected_value predicted_value
x 1800 EWR 25.28904 55.9979921
x 1800 EWR 25.17755 -0.9117075
x 1800 EWR 25.17576 53.3361651
x 1800 EWR 24.89808 18.3176746
x 1800 EWR 25.23642 -33.8479724
x 1800 EWR 25.19635 64.8123159
x 1800 EWR 25.19396 7.0235926
x 1800 EWR 25.27680 -22.0220030
x 1800 EWR 24.91373 23.1823323
x 1800 EWR 25.18631 30.6466137
x 1800 EWR 25.03615 18.8046293
x 1800 EWR 25.11585 20.3787762
x 1800 EWR 24.81270 22.9971457
x 1800 EWR 25.09939 -22.0420811
x 1800 EWR 25.05616 142.7537812
x 1800 EWR 24.96144 24.7822638
x 1800 EWR 25.12148 52.1525978
x 1800 EWR 25.09324 63.8321423
x 1800 EWR 25.24462 35.4440097
x 1800 EWR 25.27756 18.2218304
x 1800 EWR 25.35682 51.6869510
x 1800 EWR 25.03738 34.9847053
x 1800 EWR 24.93520 33.7702423
x 1800 EWR 25.07127 0.5750688
x 1800 EWR 25.12708 104.6712426
x 1800 EWR 25.06353 59.8845122
x 1800 EWR 25.15173 27.7811278
x 1800 EWR 25.18725 -10.0150814
x 1800 EWR 25.18298 39.0902563
x 1800 EWR 25.09045 -13.4855987
x 1800 EWR 24.84672 40.6034908
x 1800 EWR 25.06305 55.6640353
x 1800 EWR 25.12418 -6.7923679
x 1800 EWR 24.89454 53.5158588
x 1800 EWR 24.98407 57.4538783
x 1800 EWR 24.86451 -35.4825183
x 1800 EWR 25.29828 24.6214881
x 1800 EWR 24.99488 7.7848995
x 1800 EWR 25.18198 13.1142820
x 1800 EWR 25.20651 53.9801215
x 1800 EWR 24.92319 -17.4499215
x 1800 EWR 25.01585 13.5183136
x 1800 EWR 24.92781 29.4792351
x 1800 EWR 25.02097 1.4946316
x 1800 EWR 25.17600 18.0601691
x 1800 EWR 24.91712 52.7585700
x 1800 EWR 25.08600 17.6430963
x 1800 EWR 25.13607 8.2383583
x 1800 EWR 25.03973 11.3977432
x 1800 EWR 24.97601 57.6070933
x 1800 EWR 24.79342 88.2571213
x 1800 EWR 24.99109 30.9441666
x 1800 EWR 25.12302 12.6662259
x 1800 EWR 25.03285 53.7092555
x 1800 EWR 25.18821 15.9006947
x 1800 EWR 25.07788 22.3387812
x 1800 EWR 25.26275 50.1938404
x 1800 EWR 24.78040 -22.0861630
x 1800 EWR 25.10836 -9.3007256
x 1800 EWR 24.76158 20.8478972
x 1800 EWR 25.03824 11.8652820
x 1800 EWR 25.09167 22.3720624
x 1800 EWR 25.15623 34.9676479
x 1800 EWR 25.05061 -15.7323838
x 1800 EWR 25.11431 79.9151843
x 1800 EWR 25.26605 18.7788512
x 1800 EWR 25.27748 30.5729495
x 1800 EWR 25.28974 -30.8381265
x 1800 EWR 24.88767 20.3359572
x 1800 EWR 25.11325 69.3546678
x 1800 EWR 25.25068 71.7251724
x 1800 EWR 25.24738 7.7926146
x 1800 EWR 25.10614 39.3266608
x 1800 EWR 25.14181 87.0093584
x 1800 EWR 25.10642 69.1334004
x 1800 EWR 25.15260 84.8814005
x 1800 EWR 25.33677 22.7850458
x 1800 EWR 25.04256 21.0768844
x 1800 EWR 25.04959 43.2859183
x 1800 EWR 24.87223 54.4515221
x 1800 EWR 24.93897 13.4602208
x 1800 EWR 25.13670 14.1854907
x 1800 EWR 25.04974 -4.3859490
x 1800 EWR 25.09465 -19.0452156
x 1800 EWR 25.20593 32.6658247
x 1800 EWR 24.96386 15.6738258
x 1800 EWR 25.17890 72.9146099
x 1800 EWR 25.08935 -54.4645839
x 1800 EWR 24.99278 67.9812096
x 1800 EWR 25.06145 22.3240340
x 1800 EWR 25.17847 -12.2724239
x 1800 EWR 25.04769 3.4767257
x 1800 EWR 24.84109 -42.0206698
x 1800 EWR 24.81153 30.2210712
x 1800 EWR 25.22126 20.1737342
x 1800 EWR 24.98275 56.6414260
x 1800 EWR 24.97606 42.0233534
x 1800 EWR 25.13038 37.6717943
x 1800 EWR 24.95179 -35.5549755
x 1800 EWR 25.08705 10.3384288
x 1800 EWR 25.27866 36.2066470
x 1800 EWR 25.23091 54.7096648
x 1800 EWR 25.01593 27.6378271
x 1800 EWR 25.05921 77.0022187
x 1800 EWR 25.24259 14.6885417
x 1800 EWR 24.92995 -14.5244474
x 1800 EWR 25.04379 -8.3155577
x 1800 EWR 25.10307 27.7559510
x 1800 EWR 25.18177 13.4363724
x 1800 EWR 25.28808 100.0337520
x 1800 EWR 24.96165 -22.5910293
x 1800 EWR 25.06399 37.1772865
x 1800 EWR 25.06148 54.0708270
x 1800 EWR 25.06671 43.4214405
x 1800 EWR 25.17199 -9.5639855
x 1800 EWR 24.90825 2.9379224
x 1800 EWR 25.01046 60.3682248
x 1800 EWR 25.32767 53.8278704
x 1800 EWR 25.28277 73.3437443
x 1800 EWR 24.90370 -5.6820084
x 1800 EWR 25.20533 -14.7333257
x 1800 EWR 25.14882 -25.7202665
x 1800 EWR 25.17965 39.2154156
x 1800 EWR 25.06399 42.7735511
x 1800 EWR 25.11312 -18.8576470
x 1800 EWR 24.93088 -11.3893104
x 1800 EWR 24.89865 11.9350208
x 1800 EWR 24.96628 11.3572955
x 1800 EWR 25.30482 4.9259277
x 1800 EWR 24.91784 21.2848600
x 1800 EWR 24.92755 102.3041916
x 1800 EWR 25.22169 -89.8065757
x 1800 EWR 25.09160 84.1964148
x 1800 EWR 25.14109 65.7820646
x 1800 EWR 25.04108 1.1829994
x 1800 EWR 25.02135 0.5332714
x 1800 EWR 24.99173 1.6520981
x 1800 EWR 24.96877 7.4427608
x 1800 EWR 25.18185 45.9980334
x 1800 EWR 24.92069 109.7051299
x 1800 EWR 24.96753 84.7365963
x 1800 EWR 25.00164 38.3186288
x 1800 EWR 25.36956 75.7401279
x 1800 EWR 25.21765 -11.7146038
x 1800 EWR 24.88039 -5.0253172
x 1800 EWR 25.19541 24.8823049
x 1800 EWR 25.10257 117.4719440
x 1800 EWR 24.84377 8.4085538
x 1800 EWR 25.09038 41.5408606
x 1800 EWR 25.01093 15.7994749
x 1800 EWR 25.11900 28.2205094
x 1800 EWR 25.05105 46.0613634
x 1800 EWR 25.04996 -7.8117804
x 1800 EWR 25.06330 -10.7673690
x 1800 EWR 24.98290 40.8639211
x 1800 EWR 25.10611 30.9511972
x 1800 EWR 25.18096 10.3181390
x 1800 EWR 24.98608 -3.0728639
x 1800 EWR 24.93392 45.3405853
x 1800 EWR 25.02307 3.1157742
x 1800 EWR 25.10864 81.4893427
x 1800 EWR 25.09165 1.4819631
x 1800 EWR 24.94995 52.9440503
x 1800 EWR 24.96561 -1.5224377
x 1800 EWR 25.17313 84.4200214
x 1800 EWR 25.12472 29.4484789
x 1800 EWR 24.96028 -3.7150019
x 1800 EWR 24.83733 67.6241527
x 1800 EWR 25.07082 61.9228578
x 1800 EWR 25.01862 -4.8796249
x 1800 EWR 25.25830 -25.7798642
x 1800 EWR 25.36669 45.7137820
x 1800 EWR 25.04064 -2.2610377
x 1800 EWR 25.21695 38.7014952
x 1800 EWR 25.22223 104.8668503
x 1800 EWR 25.08143 -1.0105631
x 1800 EWR 25.05967 -12.0632983
x 1800 EWR 24.93314 18.4662929
x 1800 EWR 24.89070 26.2352860
x 1800 EWR 25.14111 56.1797747
x 1800 EWR 25.35887 75.9141797
x 1800 EWR 25.20573 55.5753174
x 1800 EWR 25.05320 -5.7848574
x 1800 EWR 25.10035 -9.9118054
x 1800 EWR 25.11106 20.5305628
x 1800 EWR 24.96168 15.1560403
x 1800 EWR 25.03354 -10.9803489
x 1800 EWR 25.13280 110.1260683
x 1800 EWR 25.01090 -19.0491348
x 1800 EWR 25.34166 6.7109586
x 1800 EWR 25.19190 22.4979962
x 1800 EWR 25.03018 15.2518766
x 1800 EWR 24.94424 28.4376706
x 1800 EWR 25.16213 52.1947235
x 1800 EWR 25.11856 -38.4709050
x 1800 EWR 24.80171 10.2836812
x 1800 EWR 25.07261 56.5000555
x 1800 EWR 24.95952 -29.7360328
x 1800 EWR 25.09245 -3.9761390
x 1800 EWR 24.96424 -85.4483947
x 1800 EWR 25.03798 44.0636728
x 1800 EWR 25.27812 15.7682555
x 1800 EWR 25.02486 -17.4717270
x 1800 EWR 25.30043 33.4143301
x 1800 EWR 25.27540 13.6748715
x 1800 EWR 24.88763 26.8696222
x 1800 EWR 25.00085 20.3950821
x 1800 EWR 25.15968 -19.6289234
x 1800 EWR 24.94829 70.4398712
x 1800 EWR 25.09457 41.0342524
x 1800 EWR 25.18822 -4.3664173
x 1800 EWR 25.08824 46.9099591
x 1800 EWR 25.16178 36.4894066
x 1800 EWR 25.18756 77.8737113
x 1800 EWR 25.04107 -6.5108547
x 1800 EWR 25.04859 -20.1845433
x 1800 EWR 25.32657 65.8045705
x 1800 EWR 25.31924 1.0783404
x 1800 EWR 24.86921 18.6550414
x 1800 EWR 25.02074 0.3334113
x 1800 EWR 25.17006 119.9640913
x 1800 EWR 25.15654 10.8541796
x 1800 EWR 25.09034 -14.9177746
x 1800 EWR 24.98515 47.9418297
x 1800 EWR 25.11868 -71.7988500
x 1800 EWR 25.11729 -23.5783590
x 1800 EWR 25.18197 22.9901774
x 1800 EWR 25.21953 -32.2073430
x 1800 EWR 25.13476 8.4069016
x 1800 EWR 25.06368 15.9594965
x 1800 EWR 25.20782 53.4621398
x 1800 EWR 25.04910 13.4905494
x 1800 EWR 24.98055 58.7628076
x 1800 EWR 25.27264 42.6200244
x 1800 EWR 25.10639 52.5953144
x 1800 EWR 25.27663 83.3632025
x 1800 EWR 25.09238 42.2919238
x 1800 EWR 25.00597 21.1003864
x 1800 EWR 25.29845 27.0240474
x 1800 EWR 25.10310 21.9110944
x 1800 EWR 25.00933 65.5683464
x 1800 EWR 25.08750 -8.6267310
x 1800 EWR 24.84214 33.1913257
x 1800 EWR 25.02242 35.7509501
x 1800 EWR 25.09416 -4.4235136
x 1800 EWR 25.11741 -23.8574651
x 1800 EWR 25.10993 29.3136074
x 1800 EWR 25.19028 58.0431005
x 1800 EWR 24.90448 42.3344625
x 1800 EWR 25.22945 0.4125113
x 1800 EWR 24.99047 -33.9241316
x 1800 EWR 24.75162 -32.7942946
x 1800 EWR 24.96648 62.8211640
x 1800 EWR 25.10579 80.4974630
x 1800 EWR 25.26683 -39.0577706
x 1800 EWR 25.30800 30.5189804
x 1800 EWR 25.17440 -25.1233502
x 1800 EWR 25.04906 -58.2524475
x 1800 EWR 25.04448 38.1207924
x 1800 EWR 25.11813 43.7282573
x 1800 EWR 25.18934 45.1611522
x 1800 EWR 25.09527 -15.5516849
x 1800 EWR 25.27305 -7.9979618
x 1800 EWR 25.05172 80.7200264
x 1800 EWR 25.13474 -110.7265025
x 1800 EWR 24.97184 -8.2268975
x 1800 EWR 25.13268 -12.8048577
x 1800 EWR 24.93158 -20.5050279
x 1800 EWR 25.08110 30.4088477
x 1800 EWR 24.98401 -42.4660983
x 1800 EWR 25.22077 40.4431909
x 1800 EWR 24.99276 83.4337933
x 1800 EWR 24.98071 64.1518182
x 1800 EWR 24.88063 14.1964111
x 1800 EWR 24.98803 -33.1851083
x 1800 EWR 24.89204 68.2892641
x 1800 EWR 25.18768 40.4210008
x 1800 EWR 24.98481 31.3556965
x 1800 EWR 25.32935 33.2069795
x 1800 EWR 24.75509 42.2328476
x 1800 EWR 25.18694 -30.3777936
x 1800 EWR 25.23067 -17.7073957
x 1800 EWR 24.97353 29.0957293
x 1800 EWR 25.25444 -30.0476140
x 1800 EWR 25.31777 38.8211528
x 1800 EWR 25.15161 13.0328098
x 1800 EWR 25.04896 63.2753384
x 1800 EWR 25.31018 47.0863322
x 1800 EWR 25.03148 -4.4079285
x 1800 EWR 24.98940 85.6651653
x 1800 EWR 25.10218 71.0611430
x 1800 EWR 25.01981 2.2172033
x 1800 EWR 24.96091 61.6823156
x 1800 EWR 25.01116 55.7764180
x 1800 EWR 25.18111 24.2765650
x 1800 EWR 25.09200 2.0299254
x 1800 EWR 25.13069 -12.6334391
x 1800 EWR 24.99979 10.4892456
x 1800 EWR 25.22636 4.0236348
x 1800 EWR 24.95228 -22.3256917
x 1800 EWR 25.03851 98.5984315
x 1800 EWR 25.11811 40.7527706
x 1800 EWR 25.18895 47.9963163
x 1800 EWR 25.07679 -12.7327115
x 1800 EWR 25.13543 44.1404513
x 1800 EWR 25.07793 22.4917305
x 1800 EWR 25.02182 73.8317315
x 1800 EWR 25.25233 88.9856672
x 1800 EWR 24.99297 82.7550480
x 1800 EWR 25.03205 18.9180814
x 1800 EWR 24.91748 29.9197074
x 1800 EWR 25.26403 70.1034830
x 1800 EWR 25.07705 20.8825377
x 1800 EWR 25.13088 40.8178051
x 1800 EWR 25.00827 59.5165779
x 1800 EWR 25.19854 73.1041401
x 1800 EWR 25.00453 111.2076581
x 1800 EWR 24.86161 12.2296000
x 1800 EWR 25.04994 -19.1343579
x 1800 EWR 25.08624 -8.3275781
x 1800 EWR 25.20036 16.3926433
x 1800 EWR 25.24448 -9.3614534
x 1800 EWR 25.24143 5.1697932
x 1800 EWR 24.89362 68.0380063
x 1800 EWR 25.03067 30.1091937
x 1800 EWR 25.09100 94.7305308
x 1800 EWR 25.29560 11.0344265
x 1800 EWR 25.13433 96.6548004
x 1800 EWR 25.21306 64.9940586
x 1800 EWR 25.12365 58.0789318
x 1800 EWR 25.09724 17.0266174
x 1800 EWR 25.18056 10.5667065
x 1800 EWR 25.22581 58.2863705
x 1800 EWR 24.90749 -12.0274862
x 1800 EWR 24.86534 82.2888251
x 1800 EWR 25.04576 1.2693165
x 1800 EWR 24.81644 58.9275780
x 1800 EWR 24.76955 43.2689198
x 1800 EWR 24.90176 54.6046662
x 1800 EWR 25.19901 9.0043624
x 1800 EWR 25.16374 16.7933289
x 1800 EWR 25.04017 15.2325122
x 1800 EWR 24.97417 38.0723093
x 1800 EWR 25.02489 -38.1400745
x 1800 EWR 25.04212 -17.5838714
x 1800 EWR 25.29206 69.7140832
x 1800 EWR 25.16816 1.1550846
x 1800 EWR 24.97084 45.3506198
x 1800 EWR 25.17057 43.9168512
x 1800 EWR 25.38354 -9.4627906
x 1800 EWR 25.21948 -32.2578410
x 1800 EWR 25.02183 5.9607000
x 1800 EWR 24.96498 62.2607994
x 1800 EWR 25.15533 -1.4617749
x 1800 EWR 24.91161 31.4485037
x 1800 EWR 25.37847 -27.8375473
x 1800 EWR 25.06243 8.9879039
x 1800 EWR 25.12202 20.0157301
x 1800 EWR 25.14279 -19.3086690
x 1800 EWR 25.01083 37.7944881
x 1800 EWR 25.07774 37.1582449
x 1800 EWR 24.97279 92.9057144
x 1800 EWR 25.21321 36.6469995
x 1800 EWR 25.06518 74.3333086
x 1800 EWR 25.04226 33.8298113
x 1800 EWR 25.16920 25.5862327
x 1800 EWR 25.11996 -4.1857507
x 1800 EWR 25.01122 99.7339077
x 1800 EWR 25.05227 30.2192791
x 1800 EWR 25.17979 -39.3596690
x 1800 EWR 25.10635 -21.6716565
x 1800 EWR 24.91269 1.4860222
x 1800 EWR 24.89869 76.0619655
x 1800 EWR 25.13445 95.4212747
x 1800 EWR 24.99516 2.7027827
x 1800 EWR 24.91749 65.0985942
x 1800 EWR 25.06792 41.9299440
x 1800 EWR 24.99550 42.7949761
x 1800 EWR 25.31694 13.9123215
x 1800 EWR 25.21578 38.5536761
x 1800 EWR 24.83538 -13.2130188
x 1800 EWR 24.93074 -0.0699896
x 1800 EWR 25.09309 89.0237091
x 1800 EWR 25.17590 -43.8936155
x 1800 EWR 25.33866 -10.4629450
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x 1800 EWR 25.05910 16.3244677
x 1800 EWR 25.02774 -36.8706708
x 1800 EWR 24.72313 42.7838742
x 1800 EWR 25.07645 56.0861445
x 1800 EWR 25.18790 96.3482123
x 1800 EWR 24.91717 27.3301936
x 1800 EWR 25.12008 79.4823137
x 1800 EWR 25.17665 32.6588032
x 1800 EWR 25.19425 10.1454567
x 1800 EWR 24.87200 -29.5926882
x 1800 EWR 25.32677 7.9161071
x 1800 EWR 25.20652 82.3742286
x 1800 EWR 25.03304 -10.1164745
x 1800 EWR 25.08580 1.4191168
x 1800 EWR 25.21286 28.4653418
x 1800 EWR 25.05057 1.4901356
x 1800 EWR 25.11898 -71.6529285
x 1800 EWR 24.97925 39.6142856
x 1800 EWR 24.92476 12.4663769
x 1800 EWR 24.95276 18.4815428
x 1800 EWR 25.03320 -7.6978122
x 1800 EWR 25.00619 19.4692769
x 1800 EWR 25.14657 82.3271191
x 1800 EWR 25.06241 -16.8616148
x 1800 EWR 25.14874 54.5431476
x 1800 EWR 24.98750 -41.5260088
x 1800 EWR 24.99397 -28.5948337
x 1800 EWR 25.27205 26.3833970
x 1800 EWR 25.26101 33.4494008
x 1800 EWR 25.16558 38.6689217
x 1800 EWR 24.84697 2.4552287
x 1800 EWR 24.88253 74.8187330
x 1800 EWR 25.17602 -23.5449277
x 1800 EWR 24.99960 -9.2988845
x 1800 EWR 25.05625 20.1559703
x 1800 EWR 25.07788 -12.2554370
x 1800 EWR 24.98817 -3.1809978
x 1800 EWR 25.01397 73.8197992
x 1800 EWR 25.12745 21.8374212
x 1800 EWR 24.93731 48.5624583
x 1800 EWR 25.04565 88.1522887
x 1800 EWR 25.24539 11.3956344
x 1800 EWR 25.15546 162.9362210
x 1800 EWR 25.14290 4.8216900
x 1800 EWR 25.18133 47.0813575
x 1800 EWR 25.05980 23.2823620
x 1800 EWR 24.95701 126.6278288
x 1800 EWR 25.24503 44.1008761
x 1800 EWR 25.09590 68.5534194
x 1800 EWR 25.06026 68.4267911
x 1800 EWR 25.13426 -0.3010158
x 1800 EWR 25.10846 -10.1252214
x 1800 EWR 25.06816 33.9117987
x 1800 EWR 25.41772 67.6258363
x 1800 EWR 25.03978 11.2920610
x 1800 EWR 25.04516 16.6042858
x 1800 EWR 25.06287 66.8660202
x 1800 EWR 24.93601 6.1471557
x 1800 EWR 25.15982 -6.9466777
x 1800 EWR 25.16227 -25.2335411
x 1800 EWR 25.08526 33.4342472
x 1800 EWR 25.08352 -27.9812759
x 1800 EWR 25.01372 32.8081699
x 1800 EWR 25.00759 69.2498364
x 1800 EWR 25.13697 -33.9112172
x 1800 EWR 25.25542 15.4678251
x 1800 EWR 25.13067 10.9999170
x 1800 EWR 25.10858 -40.0220515
x 1800 EWR 25.13110 67.5427551
x 1800 EWR 25.18787 2.7883840
x 1800 EWR 25.17551 -24.3127210
x 1800 EWR 24.98200 68.2746463
x 1800 EWR 25.22074 31.9708223
x 1800 EWR 25.26966 37.3079495
x 1800 EWR 25.12376 28.8079487
x 1800 EWR 25.12248 55.7509347
x 1800 EWR 25.19037 125.6280226
x 1800 EWR 25.22169 51.8606345
x 1800 EWR 25.28104 19.3262998
x 1800 EWR 24.92854 -18.6949648
x 1800 EWR 24.95380 26.5722135
x 1800 EWR 25.05601 27.7082520
x 1800 EWR 24.86681 21.1277869
x 1800 EWR 25.08848 17.6744850
x 1800 EWR 25.04844 19.9690168
x 1800 EWR 25.25783 -15.4409618
x 1800 EWR 25.14496 23.2301486
x 1800 EWR 24.99902 -34.0511120
x 1800 EWR 25.09436 29.3416695

Predicted values

  • Por exemplo, qual é o atraso médio para um voo das 18h de Newark?
  • Note que quaisquer variáveis que não sejam 'setx' serão definidas para a ** mediana **
flights %>% mutate(origin=as.factor(origin)) %>% 
  zelig(dep_delay ~ origin + dep_time, data=., model="ls") %>% 
  setx(origin="EWR", dep_time=1800) %>%
  sim() %>%
  zelig_qi_to_df() %>%
  summarise(avg_delay=mean(predicted_value))
avg_delay
25.33659

Predicted values

  • Por exemplo, qual é o atraso médio para um voo das 18h de Newark?
  • Note que quaisquer variáveis que não sejam 'setx' serão definidas para a ** mediana **
flights %>% mutate(origin=as.factor(origin)) %>% 
  zelig(dep_delay ~ origin + dep_time, data=., model="ls") %>% 
  setx(origin="EWR", dep_time=1800) %>%
  sim() %>%
  zelig_qi_to_df() %>%
  ggplot() + 
  geom_histogram(aes(x=predicted_value))

Predicted values

  • Qual a probabilidade de que um voo das 18h de Newark seja atrasado?
flights %>% mutate(origin=as.factor(origin)) %>% 
  mutate(Late=ifelse(dep_delay>0,1,0)) %>% 
  zelig(Late ~ origin + dep_time, data=., model="logit") %>% 
  setx(origin="EWR", dep_time=1800) %>%
  sim() %>%
  zelig_qi_to_df() %>%
  ggplot() + 
  geom_histogram(aes(x=predicted_value))

Predicted values - Logit Prediction

  • E se quisermos analisar um efeito de tratamento?
  • Se um voo de Newark for reprogramado das 18h às 14h, qual será a redução no atraso?
flights %>% mutate(origin=as.factor(origin)) %>% 
  mutate(Late=ifelse(dep_delay>0,1,0)) %>% 
  zelig(dep_delay ~ origin + dep_time, data=., model="logit") %>% 
  setx(origin="EWR", dep_time=1800) %>%
  setx1(origin="EWR", dep_time=1400) %>%
  sim() %>%
  zelig_qi_to_df() %>%
  group_by(dep_time) %>%
  summarize(avg_Late=mean(predicted_value))
dep_time avg_Late
1400 17.92157
1800 24.74863

Predicted values - Logit Prediction

  • E se quisermos analisar um efeito de tratamento?
  • Se um voo de Newark for reprogramado das 18h às 14h, qual será a redução no atraso?
flights %>% mutate(origin=as.factor(origin)) %>% 
  zelig(dep_delay ~ origin + dep_time, data=., model="ls") %>% 
  setx(origin="EWR", dep_time=1800) %>%
  setx1(origin="EWR", dep_time=1400) %>%
  sim() %>%
  zelig_qi_to_df() %>%
  ggplot() + 
  geom_density(aes(x=predicted_value,group=factor(dep_time),fill=factor(dep_time)),alpha=0.5)