Testing hypothesis: There will be no difference in beverage consumption between school A and school B
Data for each school: Sex, age, and beverage consumption frequencies of the students e.g. Fizzy drinks, water, milk (categorical).
Sex and age are significantly different between the schools (chi square, p
Sophie,
I just read it today.
For your data, my suggestions are:
Since there are four factors, school, SEX, AGE and consumption. All are categorical. Among them, only beverage consumption (BV)is response variable, hence the logistic regression should be used.
Suppose there are 4 levels in BV, with probabilities p1,p2,p3,p4 for each level. you should use multinomial logistic regression (treat BV as nominal) or ordered logistic regression (treat BV as ordinal data).
Multinomial- baseline logistic: There are three dependent functions to be used in regression: (nominal BV)
Log(p1/p4)=u1+β11*school+ β21* sex + β31*age
Log(p2/p4)= u2+β12*school+ β22* sex + β32*age
Log(p3/p4)= u3+β13*school+ β23* sex + β33*age
Where sex =1 or 0 for female or male,
If age has two levels, you need one age parameter, if age has k levels, you need k-1 parameters, for continuous age , 1 parameter.
3 interceptions and 3 sets of the above parameters to be estimated.
For ordinal BV, it is commonly used cumulative logistic function
Log(p1/(p2+p3+p4))
Log((p1+p2)/(p3+p4))
Log((p1+p2 +p3)/p4)
Using SAS;
proc logistic rorder=data;
freq count;
class school sex /param=glm;
model BV =school sex age /link=glogit;
If assuming proportional among the three functions, assume same increase for logit functions.
Log(p1/(p2+p3+p4)) treat as 0
Log((p1+p2)/(p3+p4)) treat as 1
Log((p1+p2 +p3)/p4) treat as 2
Unlike multinomial logistic, there are three interceptions and one set of parameters (1 for school, 1 for sex, 1 for continuous age or k-1 for k-level age effect.
Unlike multinomial logistic, there are three interceptions and one set of parameters (1 for school, 1 for sex, 1 for continuous age or k-1 for k-level age effect.
proc logistic ;
freq count
class school sex/param=GLM;
model BV= school sex age /link=glogit ;
Other package should have similar procesures.
Hello Sophie,
What you want is regression analysis on a categorical dependent variable (CDVMs). Please refer to the attached article by Park of how to conduct such analysis via SAS, STATA, SPSS. By the way, OLS is biased for categorical DV for violations of classical assumptions.
Richard
Hi Sophie Millar
please see follow link, it help you.
https://www.youtube.com/watch?feature=player_detailpage&v=eX2sY2La4Ew
https://www.youtube.com/watch?v=fwxFz32L-AE&feature=player_detailpage
You could also simply transform each school into a dummy variable (I'm assuming you have a large survey with lots of students from the various schools). So you would have a variable School A (and the null set "not school A") etc. for each school. Then you could run simple multivariate regression since dichotomous variables don't violate the major assumptions of linear regression models.
I'm assuming the categorical variable is an INDEPENDENT variable, being used to predict some other continuous dependent variable (drink consumption), right? If so, just use a series of dummy variables (one per school).
http://www.ats.ucla.edu/stat/stata/webbooks/reg/chapter3/statareg3.htm
I would do ANOVA for a statistical analysis on categorical variables. Good luck
What's the reason for downvote of the first reply? The attached article is quite a practical and straightforward way to carry out categorical data analysis by providing some very good example of using SAS, STATA, SPSS software. And again what's the reason for Allieu Shaw's downvote? Although ANOVA is not very efficient but still good if BLUE condition could be met and OLS assumptions are not violated. This downvote without any justification is one of the RG's big disadvantages.
To Miguel, the original post (OP) Sophie has dependent variable "Beverage Consumption Frequencies" that is either event count or nominal (explicitly stated as three categories: 1. Fizzy drinks, 2. water, 3. milk). Then, OLS is biased and inefficient because of BLUE violation. The article author Park is right about using ML as estimation method. I did not see how transformation of each school into a dummy variable could help her to better understand the underlying correlation between beverage consumption behavior (choice of beverage) and location difference (defined by proxy age and sex).
For reference on downvote without comments, refer to another post: https://www.researchgate.net/post/Whats_Your_Opinion_on_Upvote_and_Downvote
For improvement on voting system, we not only have to give out brief comments about upvote and especially downvote, but need a review board or forum moderators as well.
I understood drink type as interval measure for school (hopefully as a percent of drinks in school, since OP stated these were "frequencies"). I assumed OP was using percents of race, gender, etc as independent variables for separate models (so one OLS regression each for each different DV). I understood he question to simply be how to use school as a variable. Setting up dummy variables for each school is the standard method. I linked to a Stata discussion on the topic.
Hi Miguel,
I appreciate your clarification and explanation of your ideas. But drink type is categorical as express by the OP in parenthesis. Well, I see frequencies as events occurred over total events, however I do respect your understanding on the question. I think the question should be elaborated more along with data provided, without which it is very difficult to recommend a proper method. OP does use sex and age as IVs. From my perspective, a regression analysis as I stated would be a better way to study what the root causes are for different beverage consumption behavior.
Just want to add, Allieu's ANOVA is intended for variance study which would also be feasible if BLUE condition were met. But anyway, OP now has more options for her data. Finally, I would like to thank you all for the participation. I think we can have many suggestions but our goal is one that we help OP and each other to further understand our differences and validate our methods and of course make friends and get to know more of our colleagues from diverse background and field.
Hi Miguel,
I quote another comment from Paul R. Yarnold on addressing categorical data in this post: https://www.researchgate.net/post/Help_with_analysing_several_dummy_variables_in_SPSS_Multiple_Regression/1
"As Manfred stated, the ordinal variable number of children should not be converted into dummy-variables. Likewise, arbitrary construction of multi-category dummies should never be done, as it can induce Simpson's paradox, and can also diminish predictive accuracy even in the absence of confounding. [1,2] A vastly superior methodology for this application is available for attributes that are categorical, or that are ordered, or if a combination of categorical and ordered attributes are used. [3,4]
REFERENCES
[1] Yarnold, P.R. (1996). Characterizing and circumventing Simpson’s paradox for ordered bivariate data. Educational and Psychological Measurement, 56, 430-442.
[2] http://odajournal.com/2014/03/30/breaking-up-an-ordinal-variable-can-reduce-model-classification-accuracy/
[3] http://odajournal.com/2013/11/11/univariate-and-multivariate-analysis-of-categorical-attributes-with-many-response-categories/
[4] http://odajournal.com/2013/09/19/62/"
Sophie,
I just read it today.
For your data, my suggestions are:
Since there are four factors, school, SEX, AGE and consumption. All are categorical. Among them, only beverage consumption (BV)is response variable, hence the logistic regression should be used.
Suppose there are 4 levels in BV, with probabilities p1,p2,p3,p4 for each level. you should use multinomial logistic regression (treat BV as nominal) or ordered logistic regression (treat BV as ordinal data).
Multinomial- baseline logistic: There are three dependent functions to be used in regression: (nominal BV)
Log(p1/p4)=u1+β11*school+ β21* sex + β31*age
Log(p2/p4)= u2+β12*school+ β22* sex + β32*age
Log(p3/p4)= u3+β13*school+ β23* sex + β33*age
Where sex =1 or 0 for female or male,
If age has two levels, you need one age parameter, if age has k levels, you need k-1 parameters, for continuous age , 1 parameter.
3 interceptions and 3 sets of the above parameters to be estimated.
For ordinal BV, it is commonly used cumulative logistic function
Log(p1/(p2+p3+p4))
Log((p1+p2)/(p3+p4))
Log((p1+p2 +p3)/p4)
Using SAS;
proc logistic rorder=data;
freq count;
class school sex /param=glm;
model BV =school sex age /link=glogit;
If assuming proportional among the three functions, assume same increase for logit functions.
Log(p1/(p2+p3+p4)) treat as 0
Log((p1+p2)/(p3+p4)) treat as 1
Log((p1+p2 +p3)/p4) treat as 2
Unlike multinomial logistic, there are three interceptions and one set of parameters (1 for school, 1 for sex, 1 for continuous age or k-1 for k-level age effect.
Unlike multinomial logistic, there are three interceptions and one set of parameters (1 for school, 1 for sex, 1 for continuous age or k-1 for k-level age effect.
proc logistic ;
freq count
class school sex/param=GLM;
model BV= school sex age /link=glogit ;
Other package should have similar procesures.
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