# A tibble: 6 × 5
ytrabajocor esc edad sexo educ_simple_factor
<dbl> <dbl> <dbl> <dbl+lbl> <dbl+lbl>
1 411242 15 40 2 [2. Mujer] 3 [Superior Técnica]
2 590000 5 64 1 [1. Hombre] 1 [Menos que Media]
3 520000 12 34 1 [1. Hombre] 2 [Media Completa]
4 450000 12 30 2 [2. Mujer] 2 [Media Completa]
5 160000 10 68 2 [2. Mujer] 1 [Menos que Media]
6 580000 8 56 2 [2. Mujer] 1 [Menos que Media] Clase 6
Regresión Lineal Múltiple II
Análisis Avanzado de Datos
Gabriel Sotomayor
Evaluaciones
Tarea 2: 9 de octubre
- Regresión lineal múltiple
Informe 1: 30 de Octubre
- Regresión lineal múltiple o regresión logística
Recordatorio clase anterior
El problema del control estadístico.
El control estadístico consiste en ajustar los análisis para “controlar” el efecto de otras variables (covariadas) que podrían estar influyendo en la relación entre las variables de interés.
Ejemplo: En un estudio sobre diferencias salariales entre hombres y mujeres, las covariadas pueden incluir años de empleo o nivel educativo.
Por otro lado podemos controlar estadísticamente: Control Ajuste matemático que no requiere manipulación directa de datos o exclusión de casos. Es lo que comunmente tendremos que hacer en el contexto de estudios observacionales.
Introducción al Modelo de Regresión Múltiple
Un modelo de regresión múltiple examina la relación entre una variable dependiente y varias variables independientes o predictores.
La regresión múltiple permite controlar otras variables mientras se evalúa el efecto de una variable predictora específica.
Ejemplo: Si estudiamos la relación entre el ejercicio y la pérdida de peso, también podemos controlar la cantidad de alimentos consumidos para aislar su efecto.
Ecuación básica del modelo:
\[ Y = b_0 + b_1 X_1 + b_2 X_2 + \dots + b_k X_k + \epsilon \] Donde \(Y\) es la variable dependiente, \(b_0\) es la constante o intercepto, \(X_1, X_2, \dots X_k\) son las variables independientes, \(b_1, b_2, \dots b_k\) son los coeficientes de regresión, y \(\epsilon\) es el error.
Asociación Parcial
La asociación parcial mide la relación entre dos variables manteniendo constantes otras variables.
Ejemplo: En un estudio sobre pérdida de peso, podemos medir la relación entre la ingesta de alimentos y la pérdida de peso, controlando la cantidad de ejercicio realizado.
Objetivo de la sesión
Profundizar en el concepto de control estadístico y el uso de regresión lineal múltiple con distintos tipos de variables independientes.
Ejemplo con CASEN
Trabajaremos con CASEN utilizando como variable dependiente los ingresos del trabajo, y como variable predictora la edad y los años de escolaridad. Más adelante se utilizará el sexo y el nivel educacional por tramos para ejemplificar la introudcción de variables categóricas en modelos de regresión lineal múltiple.
Ejemplo con CASEN
| Model 1 | Model 2 | Model 3 | |
|---|---|---|---|
| (Intercept) | -272321.52*** | 729366.06*** | -742740.49*** |
| (8405.83) | (8757.98) | (14303.97) | |
| esc | 77114.51*** | 88022.20*** | |
| (656.62) | (704.29) | ||
| edad | -1403.43*** | 7681.28*** | |
| (189.32) | (189.88) | ||
| R2 | 0.13 | 0.00 | 0.15 |
| Adj. R2 | 0.13 | 0.00 | 0.15 |
| Num. obs. | 88391 | 88976 | 88391 |
| ***p < 0.001; **p < 0.01; *p < 0.05 | |||
Ejemplo con CASEN
Comparación entre regresiones simples y múltiples
- Modelo 1 (Años de Escolaridad):
- El coeficiente beta para Años de Escolaridad en el modelo simple es 77,114. Indica que por cada año adicional de escolaridad, los Ingresos del Trabajo esperados aumentan en 77,114 unidades.
- Modelo 2 (Edad):
- El coeficiente beta para Edad en el modelo simple es -1,403. Indica que por cada año adicional de edad, los Ingresos del Trabajo esperados disminuyen en 1,403 unidades.
- Modelo 3 (Años de Escolaridad + Edad):
- Al incluir ambas variables, el coeficiente para Años de Escolaridad aumenta a 88,022, mientras que el coeficiente para Edad cambia drásticamente a 7,681.
Efecto de la correlación entre Años de Escolaridad y Edad
- La correlación entre Años de Escolaridad y Edad es -0.38, lo que indica que a mayor edad, en promedio, los años de escolaridad son menores.
- En el Modelo 1, el coeficiente de Años de Escolaridad es 77,114, pero en el Modelo 3 aumenta a 88,022 al incluir Edad, debido al ajuste por la correlación entre ambas variables.
- En el Modelo 2, Edad tiene un coeficiente negativo (-1,403), pero en el Modelo 3, tras ajustar por los Años de Escolaridad, el coeficiente de Edad se vuelve positivo (7,681), lo que muestra que parte del efecto negativo inicial de la edad era por su relación con la escolaridad.
Control estadístico y parcialización
- Control estadístico:
- El proceso de parcialización consiste en aislar el efecto de una variable independiente sobre los Ingresos del Trabajo, controlando por las otras variables incluidas en el modelo.
- En el modelo múltiple, el coeficiente de cada variable refleja su efecto neto después de ajustar por las demás variables en el modelo.
- Comparación de los modelos:
- Los modelos simples no muestran apropiadamente el efecto de las variables al no tener en cuenta las relaciones entre ellas.
- El modelo múltiple, al incluir ambas variables, da una imagen más completa y precisa del impacto de cada predictor, lo que se refleja en los coeficientes beta y el incremento en el valor de \(R^2\) ajustado.
Predictores categóricos en RLM
- Predictores dicotómicos:
- Las variables dicotómicas se integran directamente en el modelo. Deben ser recodificadas a valores 0 y 1.
- Cada valor representa una categoría, por ejemplo, 0 para “No” y 1 para “Sí”.
- Interpretación: El coeficiente beta asociado a esta variable representa el cambio promedio en la variable dependiente al cambiar de la categoría 0 a la categoría 1, controlando por las demás variables del modelo.
- Transformación de predictores politómicos:
- Las variables politómicas (más de dos categorías) deben transformarse en un conjunto de variables dicotómicas o dummies.
- Se crea una variable dummy para cada categoría, excepto una que se toma como categoría de referencia.
Ejemplo de sexo e ingresos del trabajo
| Model 1 | Model 2 | Model 3 | |
|---|---|---|---|
| (Intercept) | -272321.52*** | 741995.12*** | -207194.28*** |
| (8405.83) | (3648.82) | (8426.08) | |
| esc | 77114.51*** | 80356.85*** | |
| (656.62) | (652.68) | ||
| factor(sexo)2 | -167442.22*** | -235612.34*** | |
| (5477.45) | (5113.14) | ||
| R2 | 0.13 | 0.01 | 0.16 |
| Adj. R2 | 0.13 | 0.01 | 0.16 |
| Num. obs. | 88391 | 88976 | 88391 |
| ***p < 0.001; **p < 0.01; *p < 0.05 | |||
Ejemplo de sexo e ingresos del trabajo (datos simulados)
Lógica y interpretación de predictores categóricos
- Lógica de la transformación:
- El proceso de codificación convierte una variable con \(k\) categorías en \(k - 1\) variables dummies.
- Cada una de estas dummies toma el valor 1 si la observación pertenece a esa categoría y 0 en caso contrario.
- La categoría de referencia es aquella que no tiene variable dummy y sirve como punto de comparación.
- Interpretación de los coeficientes:
- El coeficiente de cada dummy representa la diferencia promedio en la variable dependiente con respecto a la categoría de referencia.
- Si el coeficiente es positivo, la media de la variable dependiente es mayor en esa categoría en comparación con la referencia; si es negativo, la media es menor.
- Todos los efectos están ajustados por las demás variables en el modelo.
Ejemplo de niveles de escolaridad
| educ_simple_factor | dummy_media_completa | dummy_superior_tecnica | dummy_superior_profesional |
|---|---|---|---|
| Menos que Media | 0 | 0 | 0 |
| Media Completa | 1 | 0 | 0 |
| Superior Técnica | 0 | 1 | 0 |
| Superior Profesional | 0 | 0 | 1 |
Ejemplo de niveles de escolaridad
| Model 1 | Model 2 | Model 3 | |
|---|---|---|---|
| Intercepto | 729366.06 (8757.98)*** | 396916.32 (4767.94)*** | 123364.01 (11171.52)*** |
| Edad | -1403.43 (189.32)*** | 5178.45 (191.43)*** | |
| Media completa (ref. menos que media) | 128948.37 (6428.87)*** | 185782.88 (6738.36)*** | |
| Superior Técnica | 271608.14 (8629.17)*** | 344560.44 (9006.92)*** | |
| Superior Profesional | 797327.92 (7042.71)*** | 868457.15 (7490.44)*** | |
| R2 | 0.00 | 0.14 | 0.15 |
| Adj. R2 | 0.00 | 0.14 | 0.15 |
| Num. obs. | 88976 | 88406 | 88406 |
| ***p < 0.001; **p < 0.01; *p < 0.05 | |||
Interpretación de los Coeficientes Beta en Regresión Lineal Múltiple
- Tamaño y Dirección del Efecto:
- Cada coeficiente beta (\(\beta\)) indica el cambio en la variable dependiente por cada unidad de cambio en la variable independiente correspondiente.
- Dirección:
- \(\beta > 0\): Indica un efecto positivo (la variable dependiente aumenta).
- \(\beta < 0\): Indica un efecto negativo (la variable dependiente disminuye).
- Controlando por las demás variables del modelo:
- El valor de \(\beta\) refleja el efecto neto de la variable independiente, es decir, ajustado por todas las otras variables incluidas en el modelo.
- Permite evaluar el efecto aislado de cada variable independiente mientras se controlan los posibles efectos de las demás.
Interpretación de Coeficientes Beta para Variables Categóricas
- Diferencia con la Categoría de Referencia:
- El coeficiente beta para una variable categórica representa la diferencia promedio en la variable dependiente entre el grupo correspondiente y la categoría de referencia.
- Si \(\beta\) es positivo, indica que el grupo en cuestión tiene una mayor media en comparación con la categoría de referencia. Si \(\beta\) es negativo, la media es menor.
- Controlando por las demás variables del modelo:
- Al igual que en las variables continuas, los efectos están ajustados por las demás variables independientes, lo que permite interpretar el efecto de la categoría como si las otras variables permanecieran constantes.
\(R^2\) en Regresión Lineal Múltiple
- Definición de \(R^2\):
- El \(R^2\) mide la proporción de la variabilidad explicada por el modelo en relación a la variabilidad total.
- Se interpreta como el porcentaje de la variación en la variable dependiente que es explicado por las variables independientes.
\[ R^2 = 1 - \frac{\sum (y_i - \hat{y}_i)^2}{\sum (y_i - \bar{y})^2} \] - Donde: - \(\hat{y}_i\) son los valores predichos. - \(y_i\) son los valores observados. - \(\bar{y}\) es el promedio de la variable dependiente.
- Limitaciones:
- El \(R^2\) puede aumentar al agregar más predictores, incluso si no aportan significativamente al modelo.
\(R^2\) Ajustado y su Utilidad
El \(R^2\) ajustado corrige la sobreestimación del \(R^2\) al penalizar por el número de predictores en el modelo.
Tiene en cuenta tanto el número de predictores como el tamaño de la muestra.
Cálculo:
- \[ R^2_{ajustado} = 1 - \left( \frac{(1 - R^2)(n - 1)}{n - k - 1} \right) \]
- Donde:
- \(n\) es el número de observaciones.
- \(k\) es el número de predictores en el modelo.
- A diferencia del \(R^2\), el \(R^2\) ajustado disminuye si se agregan predictores que no mejoran el modelo, ayudando a evitar el sobreajuste.
- Es más útil cuando se compara la calidad de diferentes modelos con un número distinto de predictores.
Evaluación docente intermedia
Se está realizando el proceso de evaluación docente intermedia, por lo que les solicitamos que puedan contestar el siguiente formulario:
https://forms.gle/xDGewTRR5yHZkZZt9
## Profundización sobre el proceso de parcialización {.smaller background-color=“white”}
En un modelo de regresión múltiple, queremos entender cómo varios predictores afectan una variable dependiente, manteniendo constante el efecto de los demás.
- Esto significa que el coeficiente de un predictor no refleja el efecto directo de la variable original, sino lo que queda de esa variable una vez que hemos controlado el efecto de los otros predictores.
- Este proceso de “limpiar” los efectos de otras variables se llama parcialización.
¿Qué es la Parcialización?
Cuando dos variables predictoras están relacionadas entre sí (por ejemplo, escolaridad y edad), sus efectos pueden estar mezclados.
- Parcialización es el proceso de “separar” el efecto de una variable del efecto de las otras.
- El resultado es un residuo parcial, que refleja solo la parte de la variable que no está explicada por los otros predictores.
Ejemplo con CASEN
Ejemplo con CASEN
ytrabajocor edad esc mod_esc.residuals mod_edad.residuals
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6 580000 56 8 -2.94899277 6.118033237
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8 300000 73 3 -6.19426382 16.017864105
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1828 350000 63 12 1.77354268 18.798168543
1829 750000 35 12 -1.11659913 -9.201831457
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1832 400000 21 12 -2.56167004 -23.201831457
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1834 404167 48 12 0.22525242 3.798168543
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1843 200000 69 6 -3.60714122 16.277965584
1844 300000 54 12 0.84456853 9.798168543
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1853 450000 49 12 0.32847178 4.798168543
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1873 450000 32 14 0.57374282 -9.361763805
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1882 220000 44 11 -1.18762498 -1.621865284
1883 1005000 47 12 0.12203307 2.798168543
1884 713333 48 12 0.22525242 3.798168543
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1889 1800000 30 10 -3.63269588 -17.041899110
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1891 1400000 45 12 -0.08440563 0.798168543
1892 350000 54 12 0.84456853 9.798168543
1893 482000 53 12 0.74134918 8.798168543
1894 412000 44 8 -4.18762498 -5.881966763
1895 4540000 34 18 4.78018152 -1.681628499
1896 470000 41 12 -0.49728303 -3.201831457
1897 500000 53 12 0.74134918 8.798168543
1898 50000 23 12 -2.35523133 -21.201831457
1899 50000 23 14 -0.35523133 -18.361763805
1900 50000 24 12 -2.25201198 -20.201831457
1901 1333333 54 10 -1.15543147 6.958100890
1902 548503 42 14 1.60593632 0.638236195
1903 600000 46 7 -4.98118628 -5.302000589
1904 583333 63 8 -2.22645732 13.118033237
1905 300000 28 12 -1.83913458 -16.201831457
1906 945000 31 16 2.47052347 -7.521696152
1907 700000 47 15 3.12203307 7.058270022
1908 1130000 52 12 0.63812983 7.798168543
1909 700000 30 15 1.36730412 -9.941729978
1910 3600000 39 17 4.29627827 1.898337675
1911 450000 49 12 0.32847178 4.798168543
1912 300000 53 13 1.74134918 10.218202369
1913 100000 20 12 -2.66488939 -24.201831457
1914 880000 65 16 5.97998138 26.478303848
1915 500000 35 10 -3.11659913 -12.041899110
1916 380000 38 15 2.19305892 -1.941729978
1917 290000 44 12 -0.18762498 -0.201831457
1918 150000 40 12 -0.60050238 -4.201831457
1919 833 45 12 -0.08440563 0.798168543
1920 735000 47 18 6.12203307 11.318371501
1921 203667 72 5 -4.29748317 17.857931758
1922 223000 66 11 1.08320073 20.378134716
1923 2500000 48 12 0.22525242 3.798168543
1924 700000 53 12 0.74134918 8.798168543
1925 637500 24 16 1.74798802 -14.521696152
1926 220000 25 16 1.85120737 -13.521696152
1927 140000 74 17 7.90895553 36.898337675
1928 880000 44 17 4.81237502 6.898337675
1929 2008333 39 17 4.29627827 1.898337675
1930 609167 37 17 4.08983957 -0.101662325
1931 3008333 37 20 7.08983957 4.158439154
1932 1250000 34 16 2.78018152 -4.521696152
1933 1870833 37 17 4.08983957 -0.101662325
1934 1525000 29 17 3.26408477 -8.101662325
1935 1100000 31 19 5.47052347 -3.261594672
1936 2360000 37 17 4.08983957 -0.101662325
1937 2356666 36 17 3.98662022 -1.101662325
1938 1000000 26 17 2.95442672 -11.101662325
1939 2025000 25 16 1.85120737 -13.521696152
1940 360000 48 12 0.22525242 3.798168543
1941 520000 46 11 -0.98118628 0.378134716
1942 400000 35 15 1.88340087 -4.941729978
1943 400000 39 12 -0.70372173 -5.201831457
1944 658333 65 15 4.97998138 25.058270022
1945 300000 66 11 1.08320073 20.378134716
1946 350000 38 17 4.19305892 0.898337675
1947 10000 39 12 -0.70372173 -5.201831457
1948 180000 22 11 -3.45845069 -23.621865284
1949 400000 64 7 -3.12323797 12.697999411
1950 550000 56 5 -5.94899277 1.857931758
1951 200000 45 5 -7.08440563 -9.142068242
1952 150000 47 5 -6.87796693 -7.142068242
1953 280000 55 6 -5.05221212 2.277965584
1954 326250 50 12 0.43169113 5.798168543
1955 60000 18 12 -2.87132809 -26.201831457
1956 320000 32 12 -1.42625718 -12.201831457
1957 320000 55 0 -11.05221212 -6.242237374
1958 320833 65 4 -6.02001862 9.437897931
1959 320000 26 12 -2.04557328 -18.201831457
1960 700000 62 12 1.67032333 17.798168543
1961 360000 42 12 -0.39406368 -2.201831457
1962 5000 35 15 1.88340087 -4.941729978
1963 450000 49 12 0.32847178 4.798168543
1964 1160000 27 12 -1.94235393 -17.201831457
1965 400000 33 16 2.67696217 -5.521696152
1966 22000000 31 15 1.47052347 -8.941729978
1967 520000 67 8 -1.81357992 17.118033237
1968 500000 50 15 3.43169113 10.058270022
1969 150000 67 8 -1.81357992 17.118033237
1970 598333 47 8 -3.87796693 -2.881966763
1971 861333 28 17 3.16086542 -9.101662325
1972 1625000 28 20 6.16086542 -4.841560846
1973 487000 71 8 -1.40070252 21.118033237
1974 270000 42 12 -0.39406368 -2.201831457
1975 341667 36 12 -1.01337978 -8.201831457
1976 400000 46 4 -7.98118628 -9.562102069
1977 150000 43 4 -8.29084433 -12.562102069
1978 417 63 8 -2.22645732 13.118033237
1979 380000 30 16 2.36730412 -8.521696152
1980 300000 67 7 -2.81357992 15.697999411
1981 500000 66 7 -2.91679927 14.697999411
1982 400000 40 17 4.39949762 2.898337675
1983 787916 47 15 3.12203307 7.058270022
1984 450000 54 10 -1.15543147 6.958100890
1985 404167 60 12 1.46388463 15.798168543
1986 500000 62 12 1.67032333 17.798168543
1987 502500 32 14 0.57374282 -9.361763805
1988 40000 35 17 3.88340087 -2.101662325
1989 834167 34 16 2.78018152 -4.521696152
1990 296000 56 0 -10.94899277 -5.242237374
1991 613333 52 9 -2.36187017 3.538067063
1992 2070000 36 19 5.98662022 1.738405328
1993 420000 43 9 -3.29084433 -5.461932937
1994 2183333 56 16 5.05100723 17.478303848
1995 650000 27 17 3.05764607 -10.101662325
1996 1070000 46 15 3.01881372 6.058270022
1997 704167 30 14 0.36730412 -11.361763805
1998 1406667 64 10 -0.12323797 16.958100890
1999 640167 45 17 4.91559437 7.898337675
2000 400000 55 12 0.94778788 10.798168543
2001 400000 37 15 2.08983957 -2.941729978
2002 250000 49 4 -7.67152822 -6.562102069
2003 638333 46 16 4.01881372 7.478303848
2004 560000 55 8 -3.05221212 5.118033237
2005 560000 36 12 -1.01337978 -8.201831457
2006 1416667 44 15 2.81237502 4.058270022
2007 610000 58 6 -4.74255407 5.277965584
2008 308333 30 9 -4.63269588 -18.461932937
2009 150834 58 8 -2.74255407 8.118033237
2010 25000 68 17 7.28963943 30.898337675
2011 80000 58 12 1.25744593 13.798168543
2012 50000 30 12 -1.63269588 -14.201831457
2013 200000 65 7 -3.02001862 13.697999411
2014 29167 82 2 -6.26528966 23.597830278
2015 541667 49 5 -6.67152822 -5.142068242
2016 600000 39 7 -5.70372173 -12.302000589
2017 400000 37 11 -1.91016043 -8.621865284
2018 380000 35 11 -2.11659913 -10.621865284
2019 240000 64 9 -1.12323797 15.538067063
2020 350000 52 9 -2.36187017 3.538067063
2021 200000 57 8 -2.84577342 7.118033237
2022 516667 26 15 0.95442672 -13.941729978
2023 400000 48 12 0.22525242 3.798168543
2024 400000 50 8 -3.56830887 0.118033237
2025 400000 58 3 -7.74255407 1.017864105
2026 58333 29 12 -1.73591523 -15.201831457
2027 300000 30 12 -1.63269588 -14.201831457
2028 33333 53 12 0.74134918 8.798168543
2029 500000 48 8 -3.77474758 -1.881966763
2030 131667 57 7 -3.84577342 5.697999411
2031 158333 28 12 -1.83913458 -16.201831457
2032 404167 29 12 -1.73591523 -15.201831457
2033 40000 92 6 -1.23309616 39.277965584
2034 150000 21 12 -2.56167004 -23.201831457
2035 850000 31 12 -1.52947653 -13.201831457
2036 550000 43 12 -0.29084433 -1.201831457
2037 451667 24 12 -2.25201198 -20.201831457
2038 330000 42 10 -2.39406368 -5.041899110
2039 1288500 54 17 5.84456853 16.898337675
2040 850000 56 12 1.05100723 11.798168543
2041 570667 30 17 3.36730412 -7.101662325
2042 560000 39 15 2.29627827 -0.941729978
2043 781750 33 17 3.67696217 -4.101662325
2044 220000 55 15 3.94778788 15.058270022
2045 220000 25 12 -2.14879263 -19.201831457
2046 610000 33 16 2.67696217 -5.521696152
2047 600000 31 14 0.47052347 -10.361763805
2048 400000 38 12 -0.80694108 -6.201831457
2049 250000 39 10 -2.70372173 -8.041899110
2050 500000 48 12 0.22525242 3.798168543
2051 180000 67 6 -3.81357992 14.277965584
2052 200000 78 6 -2.67816706 25.277965584
2053 450000 36 12 -1.01337978 -8.201831457
2054 400000 51 17 5.53491048 13.898337675
2055 2616671 48 15 3.22525242 8.058270022
2056 1200000 49 15 3.32847178 9.058270022
2057 1200000 37 17 4.08983957 -0.101662325
2058 700000 32 17 3.57374282 -5.101662325
2059 2081667 33 17 3.67696217 -4.101662325
2060 840000 32 17 3.57374282 -5.101662325
2061 1700000 62 16 5.67032333 23.478303848
2062 1383334 55 12 0.94778788 10.798168543
2063 1183334 34 14 0.78018152 -7.361763805
2064 1166667 30 16 2.36730412 -8.521696152
2065 1000000 25 15 0.85120737 -14.941729978
2066 2332499 32 16 2.57374282 -6.521696152
2067 1730834 45 12 -0.08440563 0.798168543
2068 551666 61 12 1.56710398 16.798168543
2069 600000 32 10 -3.42625718 -15.041899110
2070 560000 29 12 -1.73591523 -15.201831457
2071 1356000 55 12 0.94778788 10.798168543
2072 1384666 53 12 0.74134918 8.798168543
2073 454167 39 10 -2.70372173 -8.041899110
2074 506250 27 15 1.05764607 -12.941729978
2075 40000 55 2 -9.05221212 -3.402169722
2076 1000000 42 12 -0.39406368 -2.201831457
2077 705000 41 12 -0.49728303 -3.201831457
2078 606667 51 13 1.53491048 8.218202369
2079 2150000 35 16 2.88340087 -3.521696152
2080 750000 32 14 0.57374282 -9.361763805
2081 500000 65 9 -1.02001862 16.538067063
2082 450500 66 9 -0.91679927 17.538067063
2083 508334 50 14 2.43169113 8.638236195
2084 500000 56 12 1.05100723 11.798168543
2085 700000 41 14 1.50271697 -0.361763805
2086 1312500 35 15 1.88340087 -4.941729978
2087 400000 56 12 1.05100723 11.798168543
2088 400000 52 12 0.63812983 7.798168543
2089 400000 34 17 3.78018152 -3.101662325
2090 508333 30 15 1.36730412 -9.941729978
2091 900000 55 10 -1.05221212 7.958100890
2092 6800000 47 13 1.12203307 4.218202369
2093 826667 22 14 -0.45845069 -19.361763805
2094 900000 44 17 4.81237502 6.898337675
2095 2033333 41 17 4.50271697 3.898337675
2096 2640000 44 26 13.81237502 19.678642112
2097 450000 42 12 -0.39406368 -2.201831457
2098 500000 24 13 -1.25201198 -18.781797631
2099 500000 20 11 -3.66488939 -25.621865284
2100 400000 32 12 -1.42625718 -12.201831457
2101 877333 44 12 -0.18762498 -0.201831457
2102 1500000 35 22 8.88340087 4.998506807
2103 380000 27 16 2.05764607 -11.521696152
2104 625000 50 12 0.43169113 5.798168543
2105 640400 58 6 -4.74255407 5.277965584
2106 500000 52 8 -3.36187017 2.118033237
2107 430000 34 12 -1.21981848 -10.201831457
2108 280000 30 12 -1.63269588 -14.201831457
2109 1008333 45 15 2.91559437 5.058270022
2110 350000 44 8 -4.18762498 -5.881966763
2111 500000 42 12 -0.39406368 -2.201831457
2112 350000 58 8 -2.74255407 8.118033237
2113 500000 33 12 -1.32303783 -11.201831457
2114 205000 28 17 3.16086542 -9.101662325
2115 250833 64 8 -2.12323797 14.118033237
2116 400000 65 8 -2.02001862 15.118033237
2117 910000 46 12 0.01881372 1.798168543
2118 200000 58 6 -4.74255407 5.277965584
2119 310000 41 9 -3.49728303 -7.461932937
2120 1345000 43 14 1.70915567 1.638236195
2121 459167 40 12 -0.60050238 -4.201831457
2122 512500 43 10 -2.29084433 -4.041899110
2123 490000 56 8 -2.94899277 6.118033237
2124 480000 45 12 -0.08440563 0.798168543
2125 1200000 45 13 0.91559437 2.218202369
2126 680000 55 12 0.94778788 10.798168543
2127 700000 36 15 1.98662022 -3.941729978
2128 750000 36 12 -1.01337978 -8.201831457
2129 453750 37 12 -0.91016043 -7.201831457
2130 500000 42 15 2.60593632 2.058270022
2131 650000 58 8 -2.74255407 8.118033237
2132 485833 54 12 0.84456853 9.798168543
2133 800000 45 12 -0.08440563 0.798168543
2134 620000 23 15 0.64476867 -16.941729978
2135 600000 50 15 3.43169113 10.058270022
2136 454000 43 15 2.70915567 3.058270022
2137 500000 32 12 -1.42625718 -12.201831457
2138 600000 59 8 -2.63933472 9.118033237
2139 700000 56 14 3.05100723 14.638236195
2140 1500000 58 17 6.25744593 20.898337675
2141 500000 25 17 2.85120737 -12.101662325
2142 400000 72 6 -3.29748317 19.277965584
2143 500000 50 16 4.43169113 11.478303848
2144 400000 65 4 -6.02001862 9.437897931
2145 400000 33 12 -1.32303783 -11.201831457
2146 150000 44 14 1.81237502 2.638236195
2147 1943333 37 19 6.08983957 2.738405328
2148 4500000 35 22 8.88340087 4.998506807
2149 1241667 28 18 4.16086542 -7.681628499
2150 400000 58 4 -6.74255407 2.437897931
2151 550000 62 6 -4.32967667 9.277965584
2152 426667 56 8 -2.94899277 6.118033237
2153 500000 51 12 0.53491048 6.798168543
2154 400000 27 12 -1.94235393 -17.201831457
2155 400000 20 14 -0.66488939 -21.361763805
2156 700000 50 14 2.43169113 8.638236195
2157 800000 48 15 3.22525242 8.058270022
2158 400000 40 12 -0.60050238 -4.201831457
2159 200000 24 15 0.74798802 -15.941729978
2160 380000 50 12 0.43169113 5.798168543
2161 912833 51 12 0.53491048 6.798168543
2162 401667 33 12 -1.32303783 -11.201831457
2163 1045333 34 17 3.78018152 -3.101662325
2164 330000 52 7 -4.36187017 0.697999411
2165 400000 54 6 -5.15543147 1.277965584
2166 400000 29 12 -1.73591523 -15.201831457
2167 500000 62 12 1.67032333 17.798168543
2168 1749310 40 16 3.39949762 1.478303848
2169 650000 38 12 -0.80694108 -6.201831457
2170 950000 35 12 -1.11659913 -9.201831457
2171 1000000 46 11 -0.98118628 0.378134716
2172 500000 64 6 -4.12323797 11.277965584
2173 450000 46 11 -0.98118628 0.378134716
2174 900000 52 8 -3.36187017 2.118033237
2175 500000 59 9 -1.63933472 10.538067063
2176 203333 55 12 0.94778788 10.798168543
2177 743333 23 13 -1.35523133 -19.781797631
2178 1305750 63 12 1.77354268 18.798168543
2179 600000 57 12 1.15422658 12.798168543
2180 415000 36 14 0.98662022 -5.361763805
2181 900000 31 12 -1.52947653 -13.201831457
2182 1000000 28 12 -1.83913458 -16.201831457
2183 2100000 28 14 0.16086542 -13.361763805
2184 1700833 35 15 1.88340087 -4.941729978
2185 1000000 32 14 0.57374282 -9.361763805
2186 1500000 43 12 -0.29084433 -1.201831457
2187 263000 32 10 -3.42625718 -15.041899110
2188 880000 38 12 -0.80694108 -6.201831457
2189 1815000 44 12 -0.18762498 -0.201831457
2190 1160000 42 12 -0.39406368 -2.201831457
2191 1180000 38 12 -0.80694108 -6.201831457
2192 150000 20 15 0.33511061 -19.941729978
2193 500000 60 12 1.46388463 15.798168543
2194 450000 37 7 -5.91016043 -14.302000589
2195 150000 35 8 -5.11659913 -14.881966763
2196 304583 41 12 -0.49728303 -3.201831457
2197 450000 43 12 -0.29084433 -1.201831457
2198 400000 58 8 -2.74255407 8.118033237
2199 200000 34 8 -5.21981848 -15.881966763
2200 65000 67 9 -0.81357992 18.538067063
2201 150000 45 5 -7.08440563 -9.142068242
2202 1283333 45 12 -0.08440563 0.798168543
2203 550000 39 12 -0.70372173 -5.201831457
2204 554167 51 12 0.53491048 6.798168543
2205 380000 45 17 4.91559437 7.898337675
2206 300000 30 14 0.36730412 -11.361763805
2207 600000 30 14 0.36730412 -11.361763805
2208 538167 38 11 -1.80694108 -7.621865284
2209 100000 45 8 -4.08440563 -4.881966763
2210 500000 20 12 -2.66488939 -24.201831457
2211 480000 33 9 -4.32303783 -15.461932937
2212 500000 65 4 -6.02001862 9.437897931
2213 900000 26 10 -4.04557328 -21.041899110
2214 400000 59 9 -1.63933472 10.538067063
2215 200000 60 8 -2.53611537 10.118033237
2216 436667 33 13 -0.32303783 -9.781797631
2217 1010000 33 12 -1.32303783 -11.201831457
2218 100000 71 2 -7.40070252 12.597830278
2219 500000 52 7 -4.36187017 0.697999411
2220 663000 47 12 0.12203307 2.798168543
2221 614000 43 12 -0.29084433 -1.201831457
2222 530000 30 12 -1.63269588 -14.201831457
2223 200000 50 12 0.43169113 5.798168543
2224 550000 36 15 1.98662022 -3.941729978
2225 2000000 73 16 6.80573618 34.478303848
2226 820000 36 17 3.98662022 -1.101662325
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[ reached 'max' / getOption("max.print") -- omitted 68392 rows ]Ejemplo con CASEN
Ejemplo con CASEN
| Model 1 | Model 2 | Model 3 | |
|---|---|---|---|
| (Intercept) | 668123.79*** | 668123.79*** | -742740.49*** |
| (2533.54) | (2726.46) | (14303.97) | |
| mod_esc.residuals | 88022.20*** | ||
| (704.54) | |||
| mod_edad.residuals | 7681.28*** | ||
| (204.41) | |||
| esc | 88022.20*** | ||
| (704.29) | |||
| edad | 7681.28*** | ||
| (189.88) | |||
| R2 | 0.15 | 0.02 | 0.15 |
| Adj. R2 | 0.15 | 0.02 | 0.15 |
| Num. obs. | 88391 | 88391 | 88391 |
| ***p < 0.001; **p < 0.01; *p < 0.05 | |||
Ejemplo con CASEN
Con el fin de comprender la lógica del proceso de parcialziación, hacemos una regresión simple de cada predictor (e.g., escolaridad) sobre los otros predictores (e.g., edad), obteniendo los residuos de estas regresiones.
Los residuos obtenidos son la parte de la variable que no está correlacionada con los otros predictores. Estos se utilizan en lugar de las variables originales en la regresión múltiple.
Al realizar una regresión de la variable dependiente (e.g., ingresos) sobre los residuos de los predictores ajustados, obtenemos los mismos coeficientes y resultados que en una regresión múltiple tradicional.
