General Linear Model

Transcripción

1 General Linear Model The GLM Multivariate procedure allows you to model the values of multiple dependent scale variables, based on their relationships to categorical and scale predictors. SPSS tutorial

2 Definitions The GLM Univariate procedure is based on the General Linear Model procedure, in which factors and covariates are assumed to have a linear relationship to the dependent variable. Factors. Categorical predictors should be selected as factors in the model. Each level of a factor can have a different linear effect on the value of the dependent variable. Fixed-effects factors are generally thought of as variables whose values of interest are all represented in the data file. Random-effects factors are variables whose values in the data file can be considered a random sample from a larger population of values. They are useful for explaining excess variability in the dependent variable.

3 Definitions Covariates. Scale predictors should be selected as covariates in the model. Within combinations of factor levels (or cells), values of covariates are assumed to be linearly correlated with values of the dependent variables. Interactions. By default, the GLM Univariate procedure produces a model with all factorial interactions, which means that each combination of factor levels can have a different linear effect on the dependent variable. Additionally, you may specify factor-covariate interactions, if you believe that the linear relationship between a covariate and the dependent variable changes for different levels of a factor.

4 Caso más simple: One-Way ANOVA You can use the One-Way ANOVA procedure to test the hypothesis that the means of two or more groups are not significantly different. One-Way ANOVA also offers: Group-level statistics for the dependent variable A test of variance equality A plot of group means Range tests, pairwise multiple comparisons, and contrasts, to describe the nature of the group differences

5 Assumptions ANOVA procedure assumes: 1. The variances of the groups are equivalent. 2. The values of errors are independent of each other across observations and the independent variables in the model. Good study design generally avoids violation of this assumption.

6 Caso Práctico 1 Endoscopic versus transaxillary thoracic sympathectomy for primary axillary and palmar hyperhidrosis and/or facial blushing: 5-year-experience. Yilmaz EN, Dur AH, Cuesta MA, Rauwerda JA. Department of Vascular Surgery, Free University Hospital, Amsterdam, The Netherlands. Thoracic sympathectomy is effective in the permanent cure of primary axillary and palmar hyperhidrosis and facial blushing, which can be so troublesome for patients that their social and professional relations can be affected. Between October 1988 and April 1994, a total of 50 thoracic sympathectomies (10 surgical and 40 endoscopic) were performed on 5 and 23 patients, respectively. The operations were performed unilaterally, followed by the contralateral intervention after a period of 6-8 weeks. The thoracic ganglia T2-T5 were resected for hyperhidrosis. If the patient suffered from blushing, the lower 1/3 of the stellate ganglion was also resected. Postoperatively, all the operated limbs were warm and dry. In the group of patients who were operated bilaterally, only one had persistent facial blushing. The efficacy for blushing in this series was therefore 93.3%. The late relapse rate of sympathetic activity was 14.3%. Compensatory sweating was seen in 67%, gustatory sweating in 37.5% and phantom sweating in 29% of the patients. None of them considered these side effects to be troublesome. Although there is no difference between transaxillary thoracic sympathectomy and the endoscopic intervention in terms of efficacy, the latter is associated with less postoperative pain, shorter hospital stay and a rapid recovery. The thoracic sympathectomy is the treatment of choice for primary hyperhidrosis and excessive facial blushing. PMID:

7 Caso Práctico 1 A partir del anteriores resultados hemos generado un estudio donde además se compara una tercera técnica, la acupuntura. La base de datos, con valores simulados está en el archivo: Ejercicio ANOVA 1.sav GRUPO (tratamiento) 0,00 Sim. tor. Transaxilar 1,00 Sim. tor. Endoscopica 2,00 acupuntura PROBLEMA 0,00 hiperhidrosis 1,00 rubor facial (blushing) AC_SI_1 Actividad simpática inicial AC_SI_2 Actividad simpática final EA1_SC Sudoración compensatoria (efecto adverso) 0,00 No 1,00 Si EA2_DP Dolor postoperatorio (efecto adverso) 0,00 No 1,00 Si EST_POST Estancia postoperatoria (días)

8 1 Cumplimiento requisitos: Homogeneidad de varianzas En un primer estudio, solo queremos analizar si existen diferencias entre los tres Grupos de tratamiento y la actividad simpática inicial. Para averiguar si la asignación a los grupos es aleatoria. Haz un gráfico como el ejemplo que se presenta al lado. Donde además de ver como se modifica la media, vemos como disminuye la Des. Est. al avanzar el estudio. En este caso no se cumple el requisito de igualdad de varianzas. Que ocurre en nuestro caso en función del gráfico creado? Comprueba tu opinión comparándola con la prueba estadística de Levene?

9 1 Cumplimiento requisitos: Homogeneidad de varianzas Como pedir la Prueba de Levene

10 2 Ejecución del análisis Seleccionamos las variables adecuadas y ejecutamos el análisis. El problema es que la conclusión en caso de ser significativa, será incompleta, ya que de los grupos comparados solo sabemos que dos son distintos entre si pero no sabemos cual.

11 3 Comparación de grupos Evidentemente, solo en el caso de un resultado significativo tenemos que realizar comparaciones parciales: Existen 2 tipos: Contrastes (donde nosotros especificamos la combinación exacta para comparar aquellos grupos que deseamos). Post-Hoc (donde escogemos los contrastes de una lista). Ejercicio: Cuales serían los contrastes para comparar acupuntura con el promedio de los otros dos tratamientos? y para comparar los dos tratamientos quirúrgicos?

12 3 Comparación de grupos Post hoc results are valid to the extent that the standard F statistic is robust to violations of assumptions. As mentioned before, the F statistic is robust to unequal variances when sample sizes are equal or nearly equal. However, when both the variances and the sample sizes differ, the standard F statistic lacks power and is prone to give incorrect results. En el ejemplo de la imagen, Es correcto seleccionar el test de Tamhane s T2, en el hipotético caso de que el test de Levene hubiese sido significativo?

13 4 Violación de las asunciones En el caso de que los tamaños de los grupos sean distintos y las varianzas distintas existe la posibilidad de usar la prueba de Welch ya que es mucho más potente que la prueba F o la de Brown-Forsythe.

14 Seleccionamos la opción Univariate y ahora se trata simplemente de situar las variables en las casillas correspondientes. Univariate ANOVA

15 OPCIONES Plots Options: Interactions Display Post Hoc Comparisons