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Análisis nivel de logro alcanzado con el examen ser bachiller en función de variables sociodemográficas

Analysis of the level of achievement of the bachelor's degree exam as a function of sociodemographic variables

¹

Tania Paulina Morocho-Barrionuevo               =       https://orcid.org/0000-00= 02-1019-6049

Escuela Superior Politécnica de Chimborazo (ESPOCH), Facultad de Ciencias, Carrera de Estadística, Riobamba, Ecuador

tpaulina.morochob@espoch.edu.ec<= /span>

²

= Carmen Estrella Morocho-Barrionuevohttps://or= cid.org/0000-0003-0050-5888

Universidad Nacional de Chimborazo (UNACH), Riobamba, Ecuador carmen.morocho@unach.edu.ec.

³

= Diana Katherine Campoverde-Santos                      https://orcid.org= /0000-0001-8538-6747

Escuela Supe= rior Politécnica de Chimborazo (ESPOCH), Facultad de Ciencias Pecuarias, Carre= ra de Medicina Veterinaria, Riobamba, Ecuador

diana.campoverde@espoch.edu.ec.

<= /o:p>

Artículo de Investigación Científica y Tecnológica

Enviado: 12/04/2022

Revisado: 27/05/2022

Aceptado: 29/06/2022

Publicado:11/07/2022

DOI: https://doi.org/10.33262/ap= .v4i3.229

<= span style=3D'font-size:12.0pt;line-height:115%;font-family:"Times New Roman",= serif; mso-fareast-font-family:Calibri;color:blue;mso-ansi-language:ES-EC'>=

Cítese:

Morocho Barrionuevo, T. P., Morocho Barrionuevo,= C. E., & Campoverde Santos, D. K. (2022). Análisis nivel de logro alcanz= ado con el examen ser bachiller en función de variables sociodemográficas . AlfaPublicaciones, 4(3), 113–129. https://doi.org/10.33262/ap= .v4i3.229

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La revista es editada por la Editorial Ciencia Digital (Editorial de prestigio registra= da en la Cámara Ecuatoriana de Libro con No de Afiliación 663) <= span style=3D'font-size:8.0pt;line-height:115%;font-family:"Times New Roman",s= erif; mso-fareast-font-family:Calibri;color:#0563C1'>www.celibro.org.ec<= /a>

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Palabras claves: Ecuador, Modelos de respuesta Ordinal, Modelos de respuesta Nominal, modelos de respuesta múltiple, Método Stepwise

Resumen

Introducción. El presente trabajo describe el model= o de regresión logística multinomial con aplicación a datos reales, utilizando= la base de datos del examen Ser bachiller – Ecuador del ańo lectivo 2018-2019 modelización el nivel de logro alcanzado en la nota del examen de grado, = en función de las variables sociodemográficas edad, sexo, provincia, tipo de financiamiento de la institución educativa y autoidentificación étnica. <= b>Objetivo. Describir uso y utilidad de los modelos de respuesta nominal y de los de respuesta ordinal, obteniendo sus mejores predictores y estableciendo sus diferencias en la modelación de los datos. Metodología. Para el cálculo se utilizó el software libre R con datos tomados d= esde el Instituto Naci= onal de Evaluación Educativa ajustando el modelo de respuesta nominal y ordinal, además aplicando el método stepwise se halla= los mejores predictores para el estudio. Resultados. <= /span>Los resultados indican una correlación positiva y significativa entre el ento= rno de control y los indicadores ROE y ROA. Conclusiones. Se pudo conc= luir mediante la aplicación del método stepwise que las variables independient= es utilizadas en el estudio son las adecuadas ya que mediante la selección automática en los modelos de respuesta tanto nominal y ordinal dan como predictoras a las mismas variables.

Keywords:= Ecuador, Ordinal Resp= onse Models, Nominal Response Models, Multiple Response Models, Stepwise Metho= d.

Abstract

Introduction. The present work describes the multinomial logistic regression model with application to real data, using the database of the Ser bachiller exam - Ecuador of the 2018-2019 school year, modeling the level of achievement reached in the grade exam grade, based on the sociodemographic variables = age, sex, province, type of financing of the educational institution and ethnic self-identification. Goal. Describe the use and usefulness of nomi= nal response models and ordinal response models, obtaining their best predict= ors and establishing their differences in data modeling. Methodology. = For the calculation, the free software R was used with data taken from the National Institute of Educational Evaluation, adjusting the nominal and ordinal response model, in addition, applying the stepwise method, the be= st predictors for the study were found. Results. The results indicate= a positive and significant correlation between the control environment and = the ROE and ROA indicators. Conclusions. It was possible to conclude through the application of the stepwise method that the independent varia= bles used in the study are the appropriate ones, since through the automatic selection in both the nominal and ordinal response models they give the s= ame variables as predictors.

&n= bsp;

&n= bsp;

Introdu= cción

En el Ecuador la educación de calidad es un derecho que todas las perso= nas poseen y que pueden acceder sin excepción alguna, según la Constitución de = la Republica.

Los niveles educativos manejados están establecidos por el Sistema Naci= onal de Educación, mismos que se encuentran divididos en tres niveles: Inicial, Básica y Bachillerato.

·&nb= sp;            =        El nivel de Educación Inicial, es el proceso de acompańamiento de nińos para el desarrollo integral de sus capacidades cognitivas, afectivas, psicomotrices, sociales e identitarias, que va desde= los 3 hasta los 5 ańos y se divide en dos subniveles (Organización de las Naciones Unidas para la Educación, Ciencia y Cultura [= UNESCO], 2019).

Inicial 1, que no es escolarizado y comprende a infantes de hasta tres = ańos.

Inicial 2, que comprende a infantes de tres a cinco ańos.

·   &nb= sp;            =     El nivel de Educación General Básica está compuesta por diez ańos de educación obligatoria en los que se refuerzan, amplían y profundizan las capacidades y competencias adquiridas, se introducen disciplinas básicas, para garantizar la diversidad cultural y lingüística, = está divida en cuatro subniveles:

Preparatoria, que corresponde al primer grado de Educación General Bási= ca y preferentemente se ofrece a los estudiantes de cinco ańos.

Básica Elemental, que corresponde al segundo, tercero y cuarto grado de Educación General Básica y preferentemente se ofrece a los estudiantes de 6= a 8 ańos.

Básica Media, que corresponde a quinto, sexto y séptimo grado de Educac= ión General Básica y preferentemente se ofrece a los estudiantes de 9 a 11 ańos= .

Básica Superior, que corresponde a octavo, noveno y décimo grados de Educación General Básica y preferentemente se ofrece a los estudiantes de 1= 2 a 14 ańos.

<= span style=3D'font-size:12.0pt;line-height:115%;font-family:Symbol;mso-fareast-f= ont-family: Symbol;mso-bidi-font-family:Symbol;mso-fareast-language:ES'>·&nb= sp;            =        El nivel de Bachillerato General Unificado compren= de tres ańos de educación obligatoria brindando una formación general y una preparación interdisciplinaria desarrollando en los estudiantes capacidades permanentes de aprendizaje y competencias ciudadanas, consta de tres cursos primero, segundo, tercero de bachillerato y preferentemente se ofrece a los estudiantes de 15 a 17 ańos.

Las edades estipuladas son sugeridas para la educación en cada nivel, s= in embargo, no se niega el acceso de los estudiantes con: necesidades educativ= as especiales, jóvenes y adultos con escolaridad inconclusa, repetición de un = ańo escolar, entre otros, permitiéndoles acceder a un grado o curso (Ministeri= o de Educación, 2015).

Desde el 2010, el Ecuador adoptó la Ley Orgánica de Educación Superior (LOES), la cual permitió la creación de la Secretaría de Educación Superior= de Ciencia y Tecnología (SENESCYT) y el Sistema Nacional de Admisión y Nivelac= ión (SNNA) que implementó el Examen Nacional de Educación Superior (ENES) como = un instrumento obligatorio para regular el acceso a la Educación Superior, per= o en el período 2016-2017, se inició la aplicación de un nuevo examen, denominado Examen Unificado Ser Bachiller, a través del cual los estudiantes obtendría= n su título de bachiller y el cupo a una universidad (Guadagni, 2006)= .

La evaluación educativa es un proceso que integra la elaboración, aplicación y análisis de instrumentos de medición, los cuales deducen las capacidades y destrezas de las personas. El instrumento de medición educati= vo tiene como función ofrecer información para la toma correcta de decisiones,= y numerosas investigaciones consideran que el examen de ingreso a la universidad es una variable imprescindible en el éxito académico del estudiante (Carrión, 2002)<= !--[if supportFields]>.

Cuando se emplean instrumentos de gran escala y de alto impacto social,= tal como los exámenes de admisión y/o aprobación de la Educación a nivel de Bachillerato, su elaboración debe ajustarse a rigurosos estándares de calid= ad (Aiken, 1996)= .

El examen Ser Bachiller es tomado a los estudiantes pertenecientes al tercero de Bachillerato General Unificado (BGU). El procedimiento para la ejecución del examen parte de la autoasignación del estudiante a una sede o= una sede preasignada, posteriormente deberán acercase según el cronograma previ= sto, puesto que hay una fecha asignada para personas con discapacidad y personas privadas de libertad, otra para la población no escolar y otra para la población escolar y personas ecuatorianas residentes en el extranjero (Secretaría de Educación Superior [SENECYT], 2019)= .

La implementación del examen Ser bachiller desde el 2017 fue concebida = para evaluar el desarrollo de las aptitudes y destrezas que deben alcanzar los estudiantes al terminal la educación intermedia, y a la vez esta evaluación contribuye al proceso de admisión a la educación superior pública. La información recopilada con este examen sirve para la formulación de mecanis= mos de mejora para la educación a nivel inicial, básico y bachillerato, enfatiz= ando en acciones de mejora para el acceso a la educación superior (Instituto Nacional para la Evaluación de la Educación [INEE], 2017).

Siendo así de gran importancia el Examen Unificado Ser bachiller para la población con el fin de continuar con su vida educativa y profesional, se t= oma como base sustentativa para el estudio la base de datos del Instituto Nacio= nal de Evaluación educativa con su respectivo diccionario de variables denomina= da “Base de datos Ser Bachiller Ańo lectivo 2018-2019”, tomada a 514852 estudiantes pertenecientes al tercero de Bachillerato, y es oportuno identificar qué factores sociodemográficos (autoidentificación étnica, regi= ón natural, tipo de financiamiento, tipo de sexo y edad) influyen en que el estudiante de educación nivel bachillerato obtengan un nivel de logro en el rendimiento académico de tipo (insuficiente, elemental, satisfactorio o excelente).

La autoidentificación étnica es una de las variables para el estudio que vislumbra a personas que se autodefinen con alguna nacional o pueblo de man= era libre y voluntaria, sea indígena, mestizo/blanco, afroecuatoriano, montubio= u otra étnia.

En relación con las regiones naturales en Ecuador se encuentra definida= por criterios de geografía física, principalmente con el clima, la vegetación, = la hidrografía de los suelos y otros. La división territorial corresponde a Co= sta, Sierra, Oriente, Insular, Otro (Instituto Naci= onal de Estadísticas y Censos [INEC], 2018).

Región Costa: Comprende más de la cuarta parte del país, es un área geográfica que se encuentra entre el Océano Pacífico y la Cordillera de los Andes, conformada por las provincias de: Esmeraldas, Manabí, Los Ríos, Santa Elena, Guayas, Santo Domingo de los Tsáchilas y El Oro.
Región Sierra: Se extiende en una doble hilera de montańas y una estrec= ha meseta conocida como el valle interandino, constituida por: Azuay, Bolívar, Cańar, Carchi, Cotopaxi, Chimborazo, Imbabura, Loja, Pichincha y Tungurahua= .

Región Oriente: Al este de los andes, se encuentra cubierta casi en su totalidad con selva, presenta gran cantidad de la flora y la fauna nativa, formada por: Morona Santiago, Napo, Orellana, Pastaza, Sucumbíos y Zamora Chinchipe.

Región Insular: Integrada por el Archipiélago de Colón, comprendida por= la Isla Isabela, Santa Cruz y San Cristóbal (Romero, 2021).

Región Zona no delimitada: Constituida por cantones que se encuentran en zonas limítrofes o fronterizas como: Loja (Macará, Sozoranga, Espíndola, Puyango, Pindal, Zapotillo, Calvas), Zamora Chinchipe (El Pangui, Yacuambi, Yantzaza, Nangaritza, Palanda, Chinchipe, Paquisha), Pastaza (Pastaza, Arajuno), Orellana (Aguarico) y Morona Santiago (Taisha, Tiwintza, Limón Indanza, San Juan Bosco, Gualaquiza).

El tipo de financiamiento de las instituciones educativas está establec= ido según su sostenimiento como público, privado y mixto o fiscomisionales.

Públicas: Son instituciones educativas financiadas por el estado.<= /o:p>

Mixto o Fiscomisionales: Estas Instituciones Educativas son de carácter religioso o laico, de derecho privado y sin fines de lucro, que garantizan = una educación gratuita y de calidad. Los centros cuentan con financiamiento tot= al o parcial del Estado (Gobierno Central a través del MinEduc).

Privado: Constituidas y administradas por personas naturales o jurídica= s de derecho privado. La educación en estas Instituciones Educativas puede ser confesional o laica.

El tipo de sexo toma hombre y mujer, y la edad va desde los 16 a los 25 ańos debido a que la población mayoritaria se encuentra entre este rango de edades (Instituto Nacional de Evaluación Educativa, 2018)= .

El nivel de logro alcanzado existe cuatro categorías consideradas dentr= o de la calificación de la prueba Ser Bachiller: “Excelente” con una calificació= n de 950 a 1.000 puntos. En esta categoría se ubica el Grupo de Alto Rendimiento, seguido de la calificación “Satisfactoria” con un puntaje de hasta 800. Lue= go sigue la categoría “Elemental” con un puntaje de hasta 700, el cual es un requisito mínimo para que el estudiante se pueda graduar. Por último, una calificación “Insuficiente” de hasta 601, aunque sea el mínimo para poder postular a la educación superior, no puede aprobar como requerimiento de ex= amen de grado (Instituto Nacional de Estadísticas y Censos [INEC= ], 2018).

El objetivo del presente trabajo es mostrar el uso y utilidad de los modelos de respuesta nominal y de los modelos de respuesta ordinal, para la modelización del nivel de logro alcanzado en la nota del examen de grado Ser Bachiller-Ecuador periodo 2018-2019, en función de las variables sociodemográficas edad, sexo, provincia, tipo de financiamiento de la institución educativa y autoidentificación étnica.

Metodol= ogía

A.     Modelos de Respuesta <= i>Múltiple=

Con una variable aleatoria de respuesta= politómica con categorías y un conjunto de variables explicativas = , los modelos= de respuesta múltiple tienen como objetivo explicar la respuesta a partir de l= as variables explicativas (Agresti, 2002).

Si se dispone de:

·     Una muestra aleatoria de tamańo con combinaciones diferentes de valores de l= as variables explicativas , .<= /p>
·      =    Una muestra aleatoria de observaciones independientes de las vari= ables de respuesta politómica para cada , con el número de observaciones que caen en la categoría de respuesta .

De tal manera que los vectores tienen distribucion= es de probabilidad multinomiales independientes,

     <= /span>                     Ecu. 1=

Verificando que:

∙    , donde

∙       y

1.&n= bsp;     Modelos logit de Respuesta Nominal

Al tener= una variable de respuesta nominal el modelo logit se formula en base a las transformaciones logit generalizadas definidas con respecto a una categoría= de referencia:

                      Ecu. 2

Se ha tomado como categoría de referencia la última, aunque en la aplicación los programas R suelen tomar la primera; para cualq= uier transformación logit para un par de categorías se puede obtener a partir de= sus transformaciones logit generalizadas asociadas en la forma (Agresti, 2002):

                              Ecu. 3<= /o:p>
2.      Modelo logit de Respuesta Ordinal=

En el caso de una variable de respuesta cualitativa ordinal se definen transformaciones logit que tienen en cuenta el orden ent= re las distintas categorías de respuesta. Se los conoce como modelos logit acumulativos y las transformaciones logit acumulativas se definen como (Agresti, 2002):

=                 <= /span>Ecu. 4

Dadas variables explicativas y observaciones diferentes <= span style=3D'mso-spacerun:yes'> el modelo logit acumulativo de efectos homogéneos es de la forma:

                                Ecu. 5=

Siendo el vector= de valores observados de las variables explicativas con el vector= de parámetros (Agresti, 2002).

a)&n= bsp; Estimación por máxima verosimilitud

Dada una muestra aleatoria de tamańo <= /span> con combinaciones diferentes de valores de= las variables explicativas , con <= ![if !msEquation]> ; y una muestra aleatoria de observaciones independientes de la varia= ble de respuesta politómica ,<= ![if !msEquation]> , la función de verosimilitud de los datos es entonce= s= (Agresti, 2002)= :<= /span><= /span>
                                        <= b>Ecu. 6

El núcleo de = la log-verosimilitud este dado:

                                            Ecu. 7

b)&n= bsp;       Significación de parámetros

La matriz de covarianzas de los estimadores de los parámetros de los distintos modelos aquí abordados es la inversa de la matriz de informació= n de Fisher dada por las derivadas parciales de segundo orden del núcleo de la verosimilitud. (Agresti, 2002)

                                      Ecu. 8

            Ecu. 9



Las raíces cuadradas de los elementos de la diagonal de esta matriz son los err= ores estándar (ASE) de los estimadores de los parámetros del modelo.<= /span>

Como estimadores de máxima verosimilitud tienen distribución normal asintótica <= w:Sdt Citation=3D"t" ID=3D"886688897">(Jobs= on, 1991).

                                             Ecu. 10

c)&n= bsp;       Bondad de ajuste: Test chi-cuadrado de razón de verosimilitudes

El estadístico de Wilks de razón de verosimilitudes para el contraste de bondad de ajuste de un modelo de regresión logística multinomial se obtiene como menos dos veces el logar= itmo del cociente entre el supremo de la verosimilitud bajo la hipótesis nula y = el supremo de la verosimilitud en la población, es decir (Jobson, 1991):

                                  Ecu.= 11

El contraste se puede expresar como:

Tasa de clasificaciones correctas=

Para cuantific= ar la bondad del ajuste global del modelo se dispone también de otra medida co= mo es la tasa de clasificaciones correctas. Es decir, a partir del modelo ajustado, se clasifica cada observación en la categoría más probable, construyendo así una matriz de clasificación observados-predichos y se util= iza el porcentaje de clasificaciones correctas como una medida de la calidad de predicción, del mismo modo que se hace en el análisis discriminante (Pando &am= p; San Martín, 2004). Se define como la proporción de individuos clasificados correctamente por el modelo y se calcula como el cociente entre el número de observaciones clasificadas correctamente y el tamańo muestral . Un individuo= es clasificado correctamente por el modelo cuando su valor observado de la variable respuesta coincide con su valor estimado por el mo= delo (Ruston, 2012).

d)&n= bsp;       Significación de variables. Contrastes condicionales de razón de verosimilitudes

Al suponer que tenemos un modelo de regresión logística multinomial que se ajusta bien y se desea contrastar= si un subconjunto de parámetros, son nulos. Sea el modelo con ese subconjunto de parámet= ros ceros.

Así que esta anidado en el modelo general . Así que planteamos el contraste:

                              Ecu. 12

e)&n= bsp;       Selección de modelos logit - Stepwise=

La selección Stepwise es el método que combina los modelos adelante y atrás, el cual se puede empezar por el modelo vacío o el completo, pero en cada paso se examinan las variables incluidas, si deben s= alir y las no seleccionadas, si deben ingresar. El método stepwise, está basado = en contrastes condicionales de razón de verosimilitudes (Hoster, 2000).

Partiendo de un modelo vacío, sólo con la constant= e, el método consiste en partir de este modelo inicial, de modo que en cada pa= so se ajustarán todos aquellos modelos que resulten de incluir cada una de las variables explicativas que no están en el modelo seleccionado en el paso anterior. Llevándose así acabo contrastes condicionales de razón de verosimilitudes que tienen en la hipótesis alternativa el modelo resultante= de la inclusión de cada variable. De modo que se seleccionarán las variables p= ara las que el constaste sea significativo, y se incluirá en modelo aquella variable asociada al mínimo de entre todos los menores o iguales que= . (Jobson, 1991).

f)&n= bsp;        Modelos con variables explicativas categóricas: variables del diseńo<= /span>

Asociadas a una variable cualitativa con categorías denotadas por , se define u= n total de variables del diseńo o variables fictici= as, se puede utilizar el método parcial o el método marginal. (Agresti, 2002).

Resulta= dos

Para conocer el nivel de l= ogro alcanzado, se analizará distintas variables sociodemográficas (edad, sexo, autoidentificación étnica, región natural y tipo de financiamiento de la institución educativa). Con las variables planteadas se desea explicar aque= llos factores que mayormente influyan en el estudio.

Los datos para utilizar corresponden a la base de datos Ser Bachiller del Instituto Nacional de Evaluación Educativa del Ecuador correspondiente al ańo lectivo 2018-2019 proporcionado por su página web (http://evaluaciones.evaluacion.gob.ec/BI/bases-de-datos-ser-bachiller/).

Los arch= ivos se encuentran divididos en diccionario de variables especificando (instituciones educativas, distrito, circuito, provincia, cantón, parroquia= ) y la base de datos (sin etiqueta inicial de fila y el resto de las filas cont= iene información registrada de cada sujeto perteneciente a la muestra). En colum= nas se encuentra la información de cada una de las variables recogidas mismas q= ue están codificadas. Inicialmente la muestra se encuentra conformada de 514852 personas y 34 variables.

Se procede a filtrar la base considerando las variables para el estu= dio y eliminando las respuestas vacías, con la base establecida se procede hace= r el cambio de nominación tomando su valor numérico por su nombre respectivo teniendo así un total de 275498 individuos y 6 variables. El estudio se realizó con base en datos agrupados mismos que constan con 6000 filas con 7 columnas, tomando la frecuencia de = cada una de las variables (ver figura 1).

La base de datos contiene:

·&nb= sp;        Varia= ble dependiente nivel de logro alcanzado siendo: 0=3Dinsuficiente, 1=3Delementa= l, 2=3Dsatisfactorio y 3=3Dexcelente.

·&nb= sp;        Varia= bles Independientes que ofrecen información sociodemográfica del individuo: edad, sexo, autoidentificación étnica, provincia y tipo de financiamiento de las instituciones educativas detallamos en la tabla 1.=

Dentro de la base tenemos variables categóricas las regiones naturales, el tipo de financiamiento, la autoidentificación étnica= , el sexo y el nivel de logro alcanzado. La herramienta que se va a utilizar para los análisis es R Studio.

Figura 1=

Datos agrupados Ser Bachiller 2018-2019

<= /p>
Tabla 1

Datos agrupados Ser Bachiller 2018-2019<= /p>

Edad

Sexo

Autoidentificación étnica

Regiones naturales

Tipo de financiamiento de la institución educativa

De 16 - 25 ańos=

1: Mujer

2: Hombre

1: Afroecuatori= ano

2: Montubio

3: Indígena

4: Mestizo/ Bla= nco

5: Otro

1: Costa

2: Sierra<= /o:p>

3: Oriente=

4: Insular=

90: Otras (Zona= No Delimitada)

1: Público (Fiscal y Municipal)=

2: Privado (Particular)

3: Mixto (Fiscomisional)

Ajuste de regre= sión de respuesta nominal

Para realizar el ajuste se tomó en cuenta= las categorías de referencia con las cuales se va a trabajar, siendo así: Para región natural, igual a Costa; para autoidentificación étnica mestizo/blanc= o, tipo de financiamiento público, tipo de sexo hombre y nivel de logro alcanz= ado insuficiente.

Se modeliza el nivel de logro alcanzad= o en función de la edad (cuantitativa), tipo de financiamiento, región natural, = tipo de sexo y autoidentificación étnica (las cuatro cualitativas). En este caso= la variable respuesta (nivel de logro alcanzado) toma cuatro v= alores que denotaremos por elemental (categoría de referencia), <= /span> insuficiente, satisfactorio, excelente (S=3D4). En la tabla 2 se presente el ajuste del modelo

Tabla 2

Datos agrupados Ser Bachiller 2018-2019<= /p>

Coeficientes:=

Elemental

Satisfactorio

Excelente

nm_regisierra

<= /span>

-1,344

<= /span>

0,665

<= /span>

1,034

nm_regiotras

<= /span>

-0,453

<= /span>

0,148=

<= /span>

-0,028

nm_regioriente

<= /span>

-0,611

<= /span>

-0,075

<= /span>

-0,812

nm_regiinsular

<= /span>

-0,992

<= /span>

0,111=

<= /span>

-0,410

financiamientoprivado

<= /span>

-0,660

<= /span>

0,955

<= /span>

1,400

financiamientomixto

<= /span>

-0,159

<= /span>

0,667=

<= /span>

1,168=

tp_sexomujer

<= /span>

-0,042

<= /span>

0,147

<= /span>

0,245

edad

<= /span>

0,224=

<= /span>

-0,407

<= /span>

-0,833

etnibbeindigena

<= /span>

0,511

<= /span>

-0,291

<= /span>

-1,054

etnibbeafroecuatoriano

<= /span>

0,281=

<= /span>

-0,451

<= /span>

-1,049

etnibbeotro

<= /span>

0,248

<= /span>

-0,245

<= /span>

-1,052

etnibbemontubio

<= /span>

0,147=

<= /span>

0,040=

<= /span>

-0,092

Intercepts:

insuficiente

satisfactorio

excelente

<= /span>



<= /span>



<= /span>



Residual Deviance:

      563519.1

AIC:

      563597.1<= span style=3D'font-size:10.0pt;line-height:115%;font-family:"Times New Roman",= serif; mso-fareast-font-family:"Times New Roman";mso-ansi-language:ES-EC;mso-far= east-language: ES-EC;mso-bidi-font-weight:bold'>

La modelización de las transformaciones logit son de la forma:<= /span>

<= /span>

Los parámetros significativos para el estudio s= on: edad, en regiones naturales (región sierra, región oriente), autoidentificación étnica, sexo, tipo de financiamiento.

Los parámetros no significativos son: región ot= ras y región insular, ya que al ser su p-valor mayor a 0.05 se acepta la hipóte= sis nula asumiendo que los dos parámetros deberían ser cero, por tal motivo no = se extraen del modelo puesto que tienen parámetros no nulos.=

El modelo logit se puede usar como tes= t de diagnóstico para clasificar las categorías de la vari= able respuesta en función de los valores de la variable explicativa (tabla 3).

Tabla 3

Tabla de clasificación del modelo nominal

insuficiente

elemental<= /span>

satisfactorio

excelente<= /span>

insuficiente

9163

41681

5854

0

elemental<= /span>

6237

73911

36332

0

satisfactorio

1467

35860

58276

0

excelente<= /span>

31

1282

5403

0

La tabla de clasificación establece cuantas veces se repite la predicción sien= do así:

·      =    Entre los individuos de logro alcanzado insuficiente, el modelo acierta en un 16,16%.

·      =    Entre los individuos de logro alcanzado elemental, el modelo acierta en un 63,45%.

·      =    Entre los individuos de logro alcanzado satisfactorio, el modelo acierta en un 20.39%.

·      =    Entre los individuos de logro alcanzado excelente, el modelo acierta en un 0%.

·      =    Entre todos los casos, el modelo acier= ta en un 51,31%.

Ajuste de regre= sión de respuesta ordinal

Para realizar el ajuste de regresión ordi= nal logit de respuesta ordinal con variables de diseńo cualitativas y cuantitat= ivas para datos agrupados con la finalidad de explicar el nivel de logro a parti= r de todas las variables, sin embargo hay que tener encuenta cuales son las categorias de referencia con las cuales se va a trabajar, siendo así: Para región natural, igual a Costa; para autoidentificación étnica mestizo/blanc= o, tipo de financiamiento público, tipo de sexo mujer y nivel de logro alcanza= do elemental. El ajuste del modelo se presenta en la tabla 4.

Tabla 4

Datos agrupados Ser Bachiller 2018-2019=

Coefficients:

Value

Std. Error

t value

P-value

nm_regisierra

1,182

0,0081

145,61

0,0000

nm_regiotras

0,374=

0,0939

3,982=

6,841e-05<= o:p>

nm_regioriente

0,302

0,0168

17,944

5,366e-72

nm_regiinsular

0,580=

0,0933

6,223=

4,892e-10<= o:p>

financiamientoprivado

1,105

0,0098

112,538

0,0000

financiamientomixto

0,644=

0,0139

46,122

0,0000

tp_sexomujer

0,122

0,0073

16,614

7,383e-89

edad

-0,382

0,0026

-144,110

0,0000

etnibbeindigena

-0,469

0,0165

-28,338

1,18e-176

etnibbeafroecuatoriano

-0,506

0,0183

-27,622

6,09e-168<= o:p>

etnibbeotro

-0,363

0,0576

-6,296

3,054e-10

etnibbemontubio

-0,095

0,0191

-4,998

5,801e-07<= o:p>

Intercepts:

Value

Std, Error

t value

P-value

insuficiente|elemental

-7,941

0,0508

-156,222

0,0000

elemental|satisfactorio

-5,702

0,0496

-115,049

0,0000

satisfactorio|excelente

-2,228

0,0503

-44,288

0,0000

Residual Deviance:
5648176,48

AIC:

568206,48

La modelización de las transformaciones logit son de la forma:<= /span>

Los parámetros significativos para el estudio son: En Regiones Naturales (región sierra, región otras, región oriente, región insular), Tipo de financiamien= to (financiamiento privado, financiamiento mixto), Tipo de Sexo (sexo hombre), Edad, Autoidentificación étnica (etnia indígena, etnia ecuatoriana, etnia o= tro, etnia montubia).

Tabla 5

Tabla de clasificación del modelo nominal

insuficiente

elemental<= /span>

satisfactorio

excelente<= /span>

insuficiente

9626

41752

5320

0

elemental<= /span>

7469

74608

34403

0

satisfactorio

1638

38798

55167

0

excelente<= /span>

31

1519

5166

0

·      =    Entre los individuos de nivel de logro alcanzado insuficiente, el modelo acierta en un 16,98%.

·      =    Entre los individuos de nivel de logro alcanzado elemental, el modelo acierta en un 64,05%.

·      =    Entre los individuos de nivel de logro alcanzado satisfactorio, el modelo acierta en un 18,97%.<= /span>

·      =    Entre los individuos de nivel de logro alcanzado excelente, el modelo acierta en un 0%.
·      =    Entre todos los casos, el modelo acier= ta en un 50,59%.

Conclusiones

De tres a cinco conclusiones las más relevant= es= Mediante la aplicación del ajuste de respuesta nominal para la proyección del nivel de logro alcanzado se analizó la incidencia de las variables sociodemográficas en la probabilidad de qu= e un estudiante de educación media obtenga un rendimiento académico insuficiente, elemental, satisfactorio o excelente en el examen Ser Bachiller en el periodo 2018-2019. Con la construcción del modelo de regresión logística y la bondad del ajuste se validó a través del méto= do de máxima verosimilitud, donde al mostrar significancia estadística no= se desestimó ninguna variable, aceptándose la hipótesis alternativa.=

Se comprobó que para el modelo de ajuste nomi= nal y ordinal las variables utilizadas son las adecuadas, llegando a esta conclusión mediante la aplicación del método stepwise ya que la selecc= ión automática de las variables independientes como predictoras son las mismas.

Se observa que en el modelo ordinal hay 15 parámetros como variables estimadas, mientras que para el modelo nomin= al hay 39 parámetros como variables por categoría estimadas, siendo así la diferencia entre el modelo nominal y el modelo ordinal.

Referencias bibliográficas
<= w:sdtPr>
Agresti, A. (2002). Categori= cal Data Analysis. New York: Willey.

Aiken, = L. (1996). México: Prentice Hall Hispanoamérica.

Hoster D., &. L. (2000). Applied Logistic Regresion. USA: Willey & Sons.=

Jobson, J. (1991). Categorical & multivariate methods. USA: Springer verlag.

Organiz= ación de las Naciones Unidas para la Educación, Ciencia y Cultura [UNESCO]. (2019). SITEAL. ECUADOR|PERFIL DE PAÍS (N.o 05/2019). SITEAL. https://siteal.iiep.unesco.org/sites/default/files/sit_informe_pdfs/dpe_e= cuador-_25_09_19.pdf

(2019). SENECYT. https://admision.senescyt.gob.ec/etapa/autoasignacion-de-sede/=

<= /span>

El artículo que se publica es de exclusiva responsabilidad de los autores y no necesariamente reflejan el pensamiento = de la Revista Alfa Publicaciones.

El artíc= ulo queda en propiedad de la revista y, por tanto, su publicación parcial y/o t= otal en otro medio tiene que ser autorizado por el director de la Revista Alfa Publicaciones.<= /o:p>

&nb= sp;

<= /o:p>

&nb= sp;

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ISSN: 2773-7330<= /span>

Vol. 4 No. 3. pp. 113 – 129. julio-septiembre 2022

   =                                                                            =

www= .alfapublicaciones.com

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                                      Vanguardia                             Página 1131

A. Modelos de Respuesta <= i>Múltiple=

1.&n= bsp; Modelos logit de Respuesta Nominal

2. Modelo logit de Respuesta Ordinal=

a)&n= bsp; Estimación por máxima verosimilitud

b)&n= bsp; Significación de parámetros

c)&n= bsp; Bondad de ajuste: Test chi-cuadrado de razón de verosimilitudes

Tasa de clasificaciones correctas=

d)&n= bsp; Significación de variables. Contrastes condicionales de razón de verosimilitudes

e)&n= bsp; Selección de modelos logit - Stepwise=

f)&n= bsp; Modelos con variables explicativas categóricas: variables del diseńo<= /span>

Ajuste de regre= sión de respuesta nominal

Ajuste de regre= sión de respuesta ordinal

Agresti, A. (2002). Categori= cal Data Analysis. New York: Willey.

	Artículo de Investigación Científica y Tecnológica Enviado: 12/04/2022 Revisado: 27/05/2022 Aceptado: 29/06/2022 Publicado:11/07/2022 DOI: https://doi.org/10.33262/ap= .v4i3.229
<= span style=3D'font-size:12.0pt;line-height:115%;font-family:"Times New Roman",= serif; mso-fareast-font-family:Calibri;color:blue;mso-ansi-language:ES-EC'>=
Cítese:		Morocho Barrionuevo, T. P., Morocho Barrionuevo,= C. E., & Campoverde Santos, D. K. (2022). Análisis nivel de logro alcanz= ado con el examen ser bachiller en función de variables sociodemográficas . AlfaPublicaciones, 4(3), 113–129. https://doi.org/10.33262/ap= .v4i3.229
		ALFA PUBLICACION= ES, es una revista multidisciplinar, trimestral, que se publicará en soporte electrón= ico tiene como misión contribuir a la formación de profesionales competentes con visión humanística y crítica que sean capac= es de exponer sus resultados investigativos y científicos en la misma medida= que se promueva mediante su intervención cambios positivos en la sociedad.&nb= sp;https://alfapublicaciones.= com La revista es editada por la Editorial Ciencia Digital (Editorial de prestigio registra= da en la Cámara Ecuatoriana de Libro con No de Afiliación 663) <= span style=3D'font-size:8.0pt;line-height:115%;font-family:"Times New Roman",s= erif; mso-fareast-font-family:Calibri;color:#0563C1'>www.celibro.org.ec<= /a>
		Esta revista está protegida bajo una licencia Creative Commons Attribution Non Commercial N= o Derivatives 4.0 International. Copia de la licencia: http://creativecommons.org= /licenses/by-nc-nd/4.0/

Coeficientes:=	Elemental	Satisfactorio	Excelente
nm_regisierra	<= /span>	-1,344	<= /span>	0,665	<= /span>	1,034
nm_regiotras	<= /span>	-0,453	<= /span>	0,148=	<= /span>	-0,028
nm_regioriente	<= /span>	-0,611	<= /span>	-0,075	<= /span>	-0,812
nm_regiinsular	<= /span>	-0,992	<= /span>	0,111=	<= /span>	-0,410
financiamientoprivado	<= /span>	-0,660	<= /span>	0,955	<= /span>	1,400
financiamientomixto	<= /span>	-0,159	<= /span>	0,667=	<= /span>	1,168=
tp_sexomujer	<= /span>	-0,042	<= /span>	0,147	<= /span>	0,245
edad	<= /span>	0,224=	<= /span>	-0,407	<= /span>	-0,833
etnibbeindigena	<= /span>	0,511	<= /span>	-0,291	<= /span>	-1,054
etnibbeafroecuatoriano	<= /span>	0,281=	<= /span>	-0,451	<= /span>	-1,049
etnibbeotro	<= /span>	0,248	<= /span>	-0,245	<= /span>	-1,052
etnibbemontubio	<= /span>	0,147=	<= /span>	0,040=	<= /span>	-0,092
Intercepts:	insuficiente	satisfactorio	excelente
<= /span>		<= /span>		<= /span>
Residual Deviance:	563519.1
AIC:	563597.1<= span style=3D'font-size:10.0pt;line-height:115%;font-family:"Times New Roman",= serif; mso-fareast-font-family:"Times New Roman";mso-ansi-language:ES-EC;mso-far= east-language: ES-EC;mso-bidi-font-weight:bold'>

	insuficiente	elemental<= /span>	satisfactorio	excelente<= /span>
insuficiente	9163	41681	5854	0
elemental<= /span>	6237	73911	36332	0
satisfactorio	1467	35860	58276	0
excelente<= /span>	31	1282	5403	0

Coefficients:	Value	Std. Error	t value	P-value
nm_regisierra	1,182	0,0081	145,61	0,0000
nm_regiotras	0,374=	0,0939	3,982=	6,841e-05<= o:p>
nm_regioriente	0,302	0,0168	17,944	5,366e-72
nm_regiinsular	0,580=	0,0933	6,223=	4,892e-10<= o:p>
financiamientoprivado	1,105	0,0098	112,538	0,0000
financiamientomixto	0,644=	0,0139	46,122	0,0000
tp_sexomujer	0,122	0,0073	16,614	7,383e-89
edad	-0,382	0,0026	-144,110	0,0000
etnibbeindigena	-0,469	0,0165	-28,338	1,18e-176
etnibbeafroecuatoriano	-0,506	0,0183	-27,622	6,09e-168<= o:p>
etnibbeotro	-0,363	0,0576	-6,296	3,054e-10
etnibbemontubio	-0,095	0,0191	-4,998	5,801e-07<= o:p>
Intercepts:	Value	Std, Error	t value	P-value
insuficiente\|elemental	-7,941	0,0508	-156,222	0,0000
elemental\|satisfactorio	-5,702	0,0496	-115,049	0,0000
satisfactorio\|excelente	-2,228	0,0503	-44,288	0,0000
Residual Deviance:	5648176,48
AIC:	568206,48