class: front .pull-left[ # Estadística Multivariada ## Valentina Andrade .small[ ## Apoyo docente ## Sociología FACSO - UChile ## 1er Sem 20201 ## [multivariada.netlify.com](https://multivariada.netlify.com) ]] .pull-right[ .right[  <br> <br> ## Práctica 6.2: Predictores categóricos 📌[URL a práctica](https://multivariada.netlify.app/assignment/06.2-code/) ] ] --- layout: true class: animated, fadeIn --- class: inverse, bottom, right, animated, slideInRight # Objetivo de la práctica Interpretar **predictores categóricos** en la regresión lineal. --- class: inverse, bottom, right, animated, slideInRight # Contenidos ### 1. Regresión con variable independiente categórica ### 2. Predictores dicotómicos ### 3. Predictores politómicos --- class: roja, bottom, right, slideInRight # 1. Regresión con variable independiente categórica --- ## Variables categóricas - Hasta el momento sólo hemos considerado variables como **continuas/intervalares**. - A menudo, las variables explicativas son de naturaleza **cualitativa o categórica**. --- ### Variables binarias / dicotómicas 🔴 🔵 - Hombre, Mujer - Vivo, Muerto - Votó, No Votó. ### Variables politómicas 🔴 🔵 🟣 🟢 - Básica, Medía, Técnica, Universitaria - Frente Amplio, Nueva Mayoría, Chile Vamos, No interesado. --- ### Un error muy común ❌ .pull-left[ <!-- --> ] .pull-right[ El scatterplot **no es muy informativo** debido a que nuestra variable independiente solamente posee dos niveles, de modo tal que la distribución de Estatus Social Subjetivo se separa en dos grandes grupos. ] --- ### Relacionar correctamente predictores categóricos ✔ .pull-left[ <!-- --> ] .pull-right[ Esto significa que tendremos dos niveles en los valores de la variable X: 0 (Hombre) y 1 (Mujer). Como mostraremos la regresión con predictores categóricos significará **contrastar medias** entre los niveles. ] --- .pull-left[ ## Predictores categóricos - Ej, Y=Estatus social subjetivo, X= sexo `$$X=1(Mujer)$$` `$$X=0(Hombre)$$` - Las variables 1/0 usualmente son llamadas variables **dummy** ] -- <br> <br> .pull-right[ Para las mujeres: `\(Y=\alpha +\beta X= \alpha+\beta\)` Para los hombres: `\(Y=\alpha +\beta X= \alpha\)` ### El coeficiente `\(\beta\)` es la **diferencia** esperada de `\(Y\)` (ingreso) entre hombres y mujeres. ] --- class: roja, bottom, right, slideInRight # 2. Predictor dicotómico --- ## Variables * [`ess`]: "Estatus Social Subjetivo: Donde se ubicaria ud. en la sociedad chilena" (0 = el nivel mas bajo; 10 = el nivel mas alto) * [`edcine`]: ¿Cuál es su nivel educacional? Indique el tipo de estudio actual (si estudia actualmente) o el último tipo aprobado (si no estudia actualmente) - **CINE 2011 (UNESCO)**. * [`sexo`]: Sexo entrevistado. * [`edad`]: ¿Cuáles su edad? (años cumplidos). --- ## Ejemplo estimación <br> .small[ .pull-left[ ```r reg1<- lm(ess ~ sexo, data=elsoc_18) ``` ```r sjPlot::tab_model(list(reg1), show.ci=FALSE, p.style = "stars", string.pred = "Predictores", string.est = "β", digits = 3, dv.labels = c("Modelo 1")) ``` ] -- .pull-right[ <table style="border-collapse:collapse; border:none;"> <tr> <th style="border-top: double; text-align:center; font-style:normal; font-weight:bold; padding:0.2cm; text-align:left; ">&nbsp;</th> <th colspan="1" style="border-top: double; text-align:center; font-style:normal; font-weight:bold; padding:0.2cm; ">Modelo 1</th> </tr> <tr> <td style=" text-align:center; border-bottom:1px solid; font-style:italic; font-weight:normal; text-align:left; ">Predictores</td> <td style=" text-align:center; border-bottom:1px solid; font-style:italic; font-weight:normal; ">&szlig;</td> </tr> <tr> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:left; ">(Intercept)</td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; ">4.339 ^***</td> </tr> <tr> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:left; ">Sexo (1=Mujer)</td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; ">0.133 ^*</td> </tr> <tr> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:left; padding-top:0.1cm; padding-bottom:0.1cm; border-top:1px solid;">Observations</td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; padding-top:0.1cm; padding-bottom:0.1cm; text-align:left; border-top:1px solid;" colspan="1">3703</td> </tr> <tr> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:left; padding-top:0.1cm; padding-bottom:0.1cm;">R² / R² adjusted</td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; padding-top:0.1cm; padding-bottom:0.1cm; text-align:left;" colspan="1">0.002 / 0.001</td> </tr> <tr> <td colspan="2" style="font-style:italic; border-top:double black; text-align:right;">* p&lt;0.05&nbsp;&nbsp;&nbsp;** p&lt;0.01&nbsp;&nbsp;&nbsp;*** p&lt;0.001</td> </tr> </table> ] ] --- ## Ejemplo estimación <br> .small[ .pull-left[ <table style="border-collapse:collapse; border:none;"> <tr> <th style="border-top: double; text-align:center; font-style:normal; font-weight:bold; padding:0.2cm; text-align:left; ">&nbsp;</th> <th colspan="1" style="border-top: double; text-align:center; font-style:normal; font-weight:bold; padding:0.2cm; ">Modelo 1</th> </tr> <tr> <td style=" text-align:center; border-bottom:1px solid; font-style:italic; font-weight:normal; text-align:left; ">Predictores</td> <td style=" text-align:center; border-bottom:1px solid; font-style:italic; font-weight:normal; ">&szlig;</td> </tr> <tr> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:left; ">(Intercept)</td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; ">4.339 ^***</td> </tr> <tr> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:left; ">Sexo (1=Mujer)</td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; ">0.133 ^*</td> </tr> <tr> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:left; padding-top:0.1cm; padding-bottom:0.1cm; border-top:1px solid;">Observations</td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; padding-top:0.1cm; padding-bottom:0.1cm; text-align:left; border-top:1px solid;" colspan="1">3703</td> </tr> <tr> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:left; padding-top:0.1cm; padding-bottom:0.1cm;">R² / R² adjusted</td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; padding-top:0.1cm; padding-bottom:0.1cm; text-align:left;" colspan="1">0.002 / 0.001</td> </tr> <tr> <td colspan="2" style="font-style:italic; border-top:double black; text-align:right;">* p&lt;0.05&nbsp;&nbsp;&nbsp;** p&lt;0.01&nbsp;&nbsp;&nbsp;*** p&lt;0.001</td> </tr> </table> ] ] -- .pull-right[ Las mujeres (sexo=1) obtienen 0.13 puntos promedio menos **en relación** a los hombres (sexo=0) en la variable de estatus social subjetivo, manteniendo las otras variables constantes. ] --- Para el caso de los **hombres** tenemos: `$$\widehat{Y}_\text{estatus} = 4.339 + 0.133 \times 0 = 4.339$$` <br> En cambio, para las **mujeres** tenemos: `$$\widehat{Y}_\text{estatus} = 4.339 + 0.133 \times 1 = 4.472$$` --- ## ¿Qué pasa si tenemos más predictores? .small[ .pull-left[ <table style="border-collapse:collapse; border:none;"> <tr> <th style="border-top: double; text-align:center; font-style:normal; font-weight:bold; padding:0.2cm; text-align:left; ">&nbsp;</th> <th colspan="1" style="border-top: double; text-align:center; font-style:normal; font-weight:bold; padding:0.2cm; ">Modelo 1</th> <th colspan="1" style="border-top: double; text-align:center; font-style:normal; font-weight:bold; padding:0.2cm; ">Modelo 2</th> </tr> <tr> <td style=" text-align:center; border-bottom:1px solid; font-style:italic; font-weight:normal; text-align:left; ">Predictores</td> <td style=" text-align:center; border-bottom:1px solid; font-style:italic; font-weight:normal; ">&szlig;</td> <td style=" text-align:center; border-bottom:1px solid; font-style:italic; font-weight:normal; ">&szlig;</td> </tr> <tr> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:left; ">(Intercept)</td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; ">4.339 ^***</td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; ">4.602 ^***</td> </tr> <tr> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:left; ">Sexo (1=Mujer)</td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; ">0.133 ^*</td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; ">0.126 ^*</td> </tr> <tr> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:left; ">Edad</td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; "></td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; ">&#45;0.006 ^***</td> </tr> <tr> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:left; padding-top:0.1cm; padding-bottom:0.1cm; border-top:1px solid;">Observations</td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; padding-top:0.1cm; padding-bottom:0.1cm; text-align:left; border-top:1px solid;" colspan="1">3703</td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; padding-top:0.1cm; padding-bottom:0.1cm; text-align:left; border-top:1px solid;" colspan="1">3703</td> </tr> <tr> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:left; padding-top:0.1cm; padding-bottom:0.1cm;">R² / R² adjusted</td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; padding-top:0.1cm; padding-bottom:0.1cm; text-align:left;" colspan="1">0.002 / 0.001</td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; padding-top:0.1cm; padding-bottom:0.1cm; text-align:left;" colspan="1">0.005 / 0.004</td> </tr> <tr> <td colspan="3" style="font-style:italic; border-top:double black; text-align:right;">* p&lt;0.05&nbsp;&nbsp;&nbsp;** p&lt;0.01&nbsp;&nbsp;&nbsp;*** p&lt;0.001</td> </tr> </table> ] .pull-right[ Al controlar por la **edad** de las personas, **las mujeres tienen un promedio 0.126 más alto que el de los hombres** en la escala de Estatus Social Subjetivo. Vemos que, en comparación con el Modelo 1, la diferencia en el promedio de estatus subjetivo de mujeres respecto de hombres se ajusta al incorporar la *edad*. ] <br> $$\widehat{Y}_\text{estatus} = 4.602 + 0.126 \times \text{Sexo} + -0.006 \times \text{Edad} + \epsilon $$] --- class: roja, bottom, right, slideInRight # 3. Predictor politómico --- ## 3. Predictor politómico - ¿Qué sucede cuando quiero predecir el estatus social subjetivo en base una variable catégorica con **más de dos valores**? - Ej. Niveles educacionales, clase social, posición política. - Para poder trabajar correctamente los predictores categóricos en la regresión, en R la manera más simple es definirlos como un **factor**. --- ## Paso 1: ¿Cuál es la clase de mi variable? .small[ ```r elsoc_18$ed_cine <- as.numeric(elsoc_18$edcine) ``` ```r str(elsoc_18$ed_cine) ``` ``` ## num [1:3703] 2 3 3 4 3 3 3 4 5 2 ... ``` ] --- ### Si corremos la regresión tal como está .small[ .pull-left[ ```r reg3<- lm(ess~ed_cine,data = elsoc_18) ``` <table style="border-collapse:collapse; border:none;"> <tr> <th style="border-top: double; text-align:center; font-style:normal; font-weight:bold; padding:0.2cm; text-align:left; ">&nbsp;</th> <th colspan="1" style="border-top: double; text-align:center; font-style:normal; font-weight:bold; padding:0.2cm; ">Modelo 3</th> </tr> <tr> <td style=" text-align:center; border-bottom:1px solid; font-style:italic; font-weight:normal; text-align:left; ">Predictores</td> <td style=" text-align:center; border-bottom:1px solid; font-style:italic; font-weight:normal; ">&szlig;</td> </tr> <tr> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:left; ">(Intercept)</td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; ">3.329 ^***</td> </tr> <tr> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:left; ">ed_cine</td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; ">0.331 ^***</td> </tr> <tr> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:left; padding-top:0.1cm; padding-bottom:0.1cm; border-top:1px solid;">Observations</td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; padding-top:0.1cm; padding-bottom:0.1cm; text-align:left; border-top:1px solid;" colspan="1">3703</td> </tr> <tr> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:left; padding-top:0.1cm; padding-bottom:0.1cm;">R² / R² adjusted</td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; padding-top:0.1cm; padding-bottom:0.1cm; text-align:left;" colspan="1">0.064 / 0.064</td> </tr> <tr> <td colspan="2" style="font-style:italic; border-top:double black; text-align:right;">* p&lt;0.05&nbsp;&nbsp;&nbsp;** p&lt;0.01&nbsp;&nbsp;&nbsp;*** p&lt;0.001</td> </tr> </table> ]] .pull-right[ - El coeficiente de regresión nos indica que por cada nivel adicional de educación, hay un aumento de **0.331 puntos** en la escala de estatus social subjetivo. - Decir "por cada nivel educacional" es poco informativo ] --- ## Paso 2: Transformar variable con `as_factor()` - `as_factor()` de la librería `sjlabelled` - ⚠ no es lo mismo `as_factor()` que `as.factor()` ```r elsoc_18$edcine<- as_factor(elsoc_18$edcine) ``` --- ## Paso 3: Estimar el modelo ```r reg4 <- lm(ess~edcine,data = elsoc_18) ``` ```r reg4 <- lm(ess~as_factor(edcine),data = elsoc_18) ``` --- .small[ <table style="border-collapse:collapse; border:none;"> <tr> <th style="border-top: double; text-align:center; font-style:normal; font-weight:bold; padding:0.2cm; text-align:left; ">&nbsp;</th> <th colspan="1" style="border-top: double; text-align:center; font-style:normal; font-weight:bold; padding:0.2cm; ">Modelo 3</th> <th colspan="1" style="border-top: double; text-align:center; font-style:normal; font-weight:bold; padding:0.2cm; ">Modelo 4</th> </tr> <tr> <td style=" text-align:center; border-bottom:1px solid; font-style:italic; font-weight:normal; text-align:left; ">Predictores</td> <td style=" text-align:center; border-bottom:1px solid; font-style:italic; font-weight:normal; ">&szlig;</td> <td style=" text-align:center; border-bottom:1px solid; font-style:italic; font-weight:normal; ">&szlig;</td> </tr> <tr> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:left; ">(Intercept)</td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; ">3.329 ^***</td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; ">3.794 ^***</td> </tr> <tr> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:left; ">ed_cine</td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; ">0.331 ^***</td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; "></td> </tr> <tr> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:left; ">Educación: Primaria y<br>secundaria baja</td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; "></td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; ">0.151 </td> </tr> <tr> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:left; ">Educación: Secundaria<br>alta</td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; "></td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; ">0.476 ^***</td> </tr> <tr> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:left; ">Educación: Terciaria<br>ciclo corto</td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; "></td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; ">0.811 ^***</td> </tr> <tr> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:left; ">Educación: Terciaria y<br>Postgrado</td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; "></td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; ">1.279 ^***</td> </tr> <tr> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:left; padding-top:0.1cm; padding-bottom:0.1cm; border-top:1px solid;">Observations</td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; padding-top:0.1cm; padding-bottom:0.1cm; text-align:left; border-top:1px solid;" colspan="1">3703</td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; padding-top:0.1cm; padding-bottom:0.1cm; text-align:left; border-top:1px solid;" colspan="1">3703</td> </tr> <tr> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:left; padding-top:0.1cm; padding-bottom:0.1cm;">R² / R² adjusted</td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; padding-top:0.1cm; padding-bottom:0.1cm; text-align:left;" colspan="1">0.064 / 0.064</td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; padding-top:0.1cm; padding-bottom:0.1cm; text-align:left;" colspan="1">0.066 / 0.065</td> </tr> <tr> <td colspan="3" style="font-style:italic; border-top:double black; text-align:right;">* p&lt;0.05&nbsp;&nbsp;&nbsp;** p&lt;0.01&nbsp;&nbsp;&nbsp;*** p&lt;0.001</td> </tr> </table> ] --- ## Interpretación 📝 - La categoría ausente en el modelo es la **categoría de referencia** para la intepretación -- - El *coeficiente* de la variable dummy corresponde a su **diferencia** respecto de la categoría de referencia (en relación a la variable dependiente `\(Y\)`) -- - La decisión de qué categoría es la referencia obedece a la mejor **interpretación** --- ## 🎁 Bonus: Redefinir la categoría de referencia `relevel` - Alternativamente es posible cambiar la categoría de referencia. Por ejemplo, si quisieramos que la referencia fuera el nivel educativo más alto "Terciaria y Postgrado" (5) debemos usar `ref_lvl(edcine, ref =5)`: ```r reg4.1 <- lm(ess~ref_lvl(edcine,lvl=5),data = elsoc_18) ``` --- .small[ <table style="border-collapse:collapse; border:none;"> <tr> <th style="border-top: double; text-align:center; font-style:normal; font-weight:bold; padding:0.2cm; text-align:left; ">&nbsp;</th> <th colspan="1" style="border-top: double; text-align:center; font-style:normal; font-weight:bold; padding:0.2cm; ">Modelo 4</th> <th colspan="1" style="border-top: double; text-align:center; font-style:normal; font-weight:bold; padding:0.2cm; ">Modelo 4.1</th> </tr> <tr> <td style=" text-align:center; border-bottom:1px solid; font-style:italic; font-weight:normal; text-align:left; ">Predictores</td> <td style=" text-align:center; border-bottom:1px solid; font-style:italic; font-weight:normal; ">&szlig;</td> <td style=" text-align:center; border-bottom:1px solid; font-style:italic; font-weight:normal; ">&szlig;</td> </tr> <tr> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:left; ">(Intercept)</td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; ">3.794 ^***</td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; ">5.073 ^***</td> </tr> <tr> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:left; ">Educación: Primaria y<br>secundaria baja</td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; ">0.151 </td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; "></td> </tr> <tr> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:left; ">Educación: Secundaria<br>alta</td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; ">0.476 ^***</td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; "></td> </tr> <tr> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:left; ">Educación: Terciaria<br>ciclo corto</td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; ">0.811 ^***</td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; "></td> </tr> <tr> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:left; ">Educación: Terciaria y<br>Postgrado</td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; ">1.279 ^***</td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; "></td> </tr> <tr> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:left; ">Educación: Primaria<br>incompleta menos</td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; "></td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; ">&#45;1.279 ^***</td> </tr> <tr> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:left; ">Educación: Primaria y<br>secundaria baja</td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; "></td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; ">&#45;1.128 ^***</td> </tr> <tr> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:left; ">Educación: Secundaria<br>alta</td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; "></td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; ">&#45;0.803 ^***</td> </tr> <tr> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:left; ">Educación: Terciaria<br>ciclo corto</td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; "></td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; ">&#45;0.468 ^***</td> </tr> <tr> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:left; padding-top:0.1cm; padding-bottom:0.1cm; border-top:1px solid;">Observations</td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; padding-top:0.1cm; padding-bottom:0.1cm; text-align:left; border-top:1px solid;" colspan="1">3703</td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; padding-top:0.1cm; padding-bottom:0.1cm; text-align:left; border-top:1px solid;" colspan="1">3703</td> </tr> <tr> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:left; padding-top:0.1cm; padding-bottom:0.1cm;">R² / R² adjusted</td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; padding-top:0.1cm; padding-bottom:0.1cm; text-align:left;" colspan="1">0.066 / 0.065</td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; padding-top:0.1cm; padding-bottom:0.1cm; text-align:left;" colspan="1">0.066 / 0.065</td> </tr> <tr> <td colspan="3" style="font-style:italic; border-top:double black; text-align:right;">* p&lt;0.05&nbsp;&nbsp;&nbsp;** p&lt;0.01&nbsp;&nbsp;&nbsp;*** p&lt;0.001</td> </tr> </table> ] --- class: inverse ## Resumen predictores categóricos - Predictores categóricos se especifican como **variables dicotómicas** (valores 1/0, presencia/ausencia del atributo) o **politómicas** (varios niveles) -- - La variable que no ingresa al modelo es la **categoría de referencia**. También se puede pre-definir la categoría de referencia -- - El *coeficiente* de la variable dummy corresponde a su **diferencia** respecto de la categoría de referencia (en relación a la variable dependiente `\(Y\)`) --- class: front .pull-left[ # Estadística Multivariada ## Valentina Andrade .small[ ## Apoyo docente ## Sociología FACSO - UChile ## 1er Sem 20201 ## [multivariada.netlify.com](https://multivariada.netlify.com) ]] .pull-right[ .right[  <br> <br> ## Práctica 6.2: Predictores categóricos 📌[URL a práctica](https://multivariada.netlify.app/assignment/06.2-code/) ] ]