A Course in Statistical Modelling

Transcription

1 A Course in Statistical Modelling January 15, 16 and 17, Graeme Hutcheson Manchester Institute of Education, University of Manchester Exercise: Modelling ordered and unordered data. This exercise is designed to provide some experience with running and interpreting logit regression models for ordered and unordered categorical response variables (proportional odds models and multinomial logistic regression). It is designed to allow participants to experiment with using the logit models rather than to provide any sort of definitive analysis of the data. The tourist data set The data set Tourist.csv contains a sample of data collected from tourists at airports in Portugal. The dtata are available on the course CD, or can be downloaded from Training.net/Tourists.csv The data set includes information on a number of variables that were elicited from 4742 tourists (after missing data removed). The variables in the data set are: Age Country Language (coded as ordered and continuous) Qualification (coded as continuous, ordered and unordered)

2 Salary Gender Language represents the importance an individual places on the destination population being able to understand his/her native language. Qualification variable represents the qualification level of the individual, according to the following code (lower than 4 th grade = 1, 4 th grade = 2, 6 th grade = 3, 9 th grade = 4, complete high, school = 5, degree = 6, masters/phd = 7). This variable is coded as a continuous, ordered and as a collapsed category representing just 3 ordered categories (select which one you think best represents the data). The object of this exercise is to just run quick analyses and play around with the results and explore possible interpretations you should not think of these in any way as final models. Choose whether you want to model ordered or unordered variables load the data and see how far you get!

3 A Proportional Odds model. You are interested (yes you are!) in finding out whether certain types of people in your sample are more or less language-phobic than others (i.e., might the language capabilities at the destination affect where people choose to go on holiday?). Run a proportional odds model of Language.ord using Age, Country, Gender, Qualification.ord and Salary as explanatory variables. The model entered into the multinomial function should be: Language.ord ~ Age + Country + Gender + qualif.cont + Salary Use the standard output and effect plots to try and make sense of these data... The types of questions you might ask of the data are: Which variables appear to be significantly related to importance of language? What is the relationship between country and language? Which countries appear to regard language as the most and least important? Is it younger or older people who rate language as important? What is the relationship between Salary and Language? Do you think that the data for Irlanda should be combined with Inglaterra? Do your results make sense? Are they what you expected? Testing the proportional odds assumption for this model. The appropriateness of running a proportional odds model on these data can be assessed by comparing the model-fit statistics for an ordered and unordered model. This can be achieved for the current model by cutting and pasting the code below into the Rconsole (make sure that the data have been loaded in R and named Tourists ).

4 Note: The results of this analysis are provided below (the chi-square test) you do not need to compute this for now... Load the data under the name Tourists Run the unorderded model multinomial.model < multinom(language.ord ~ Age + Country + Gender + Qualif.ord + Salary, data=tourists, trace=false) Run the ordered model ordered.model < polr(language.ord ~ Age + Country + Gender + Qualif.ord + Salary, method="logistic", data=tourists, Hess=TRUE) Load the parlines function parlines< function(mod1, mod2){ dev2< deviance(mod1) dev< deviance(mod2) d< abs(mod1$edf mod2$edf) ch2< abs(dev2 dev) p< 1 pchisq(ch2, d) output< round(cbind(ch2, d, p),5) dimnames(output)[[2]]< c("chi square", "df", "p value") output } Run the parlines function parlines(multinomial.model, ordered.model) The output of the parlines test is shown below; > parlines(multinomial.model, ordered.model) Chi square df p value [1,] What does this result suggest? Could you have arrived at this conclusion by just looking at the effect displays? What might you do now (i.e., options for analysis)?

5 A Multinomial Logistic Regression Model. You are interested (You, or you funders) in finding out the profile of the nationalities of people entering Portugal. For example, does Portugal attract different types of tourist from different countries? Run a multinomial logistic regression model of Country using Age, Gender, Qualification.cont and Salary as explanatory variables. The model representation is: Country ~ Age + Gender + qualif.cont + Salary Use the standard output and effect plots to try and make sense of these data... Which variables appear to be significantly related to a tourists' country of origin? What is the relationship between country and Age? What is the relationship between Salary and Country? What is the relationship between Qualification and Country? What is the relationship between Gender and Country? What is it about Ireland? Do these results make sense? Are they what you might have expected? There are clearly many relationships in the data only some of which are likely to be usefully applied to the population. The results above will suggest some interesting relationships, but one would need to spend substantial time in refining any models. The important thing to realise is that it is relatively easy to analyse and explore these data using GLM models... Keep in mind... NOT ALL DATA ARE WORTH ANALYSING!