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I have three variables,
1. Irrational Beliefs (Categorical)
2. Anxiety State/ Trait (Categorical)
3. Personality Traits (Categorical)
Which statistical analyses can be used?

Neelam
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    Huh... You should add a little bit of contextual information here, e.g. at least specify your working hypotheses. – chl Oct 20 '10 at 19:39
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    Definitely needs more information. – Shane Oct 20 '10 at 19:41
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    And a question mark... fixed. –  Oct 20 '10 at 20:18
  • (1) presumably you have three groups of variables and within each group, you have multiple variables (e.g., perhaps you have the Big 5 factors of personality within the personality group); (2) calling your variables categorical makes people think of 'unordered categorical' when the variables are probably best treated as numeric. Thus, in addition to providing more information, you may wish to change the title of your question. – Jeromy Anglim Oct 21 '10 at 08:14
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    I'm inclined to close this question if further information isn't provided. At present it's impossible to see what is being asked. – csgillespie Oct 21 '10 at 13:43

2 Answers2

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@onestop is literally correct. If you have three unordered categorical variables, techniques like loglinear modelling are appropriate.

@Neelam However, I doubt that your data is unordered categorical.

From my experience with measures of psychological scales measuring irrational beliefs, anxiety states and traits, and personality traits, the scales are numeric.

For example, a typical personality scale might have 10 items with each item measured on a 5-point scale. Thus, if you were to sum the scale you get scores ranging from a minimum possible score of 10 to a maximum possible score of 50. I.e., there are 41 possible values. Thus, in some sense the variables are categorical, but they are also ordinal, and they are also typically treated as numeric variables. See my comments to this earlier question regarding discrete and continuous variables.

Thus, in the empirical research that I read with similar scales, researchers typically treat such scales as numeric variables. Thus, methods such as correlation, regression, and PCA are standard.

Community
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Jeromy Anglim
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  • I like this. I would add that (1) the OP is likely to be interested in studying asymmetrical relationships between all three variables, so that a SEM approach would make sense; proceeding this way would also (2) allow to account for specific measurement error at the level of the scales. – chl Oct 21 '10 at 07:27
  • Thank You Jeromy for clearing the concept. I am really grateful. Can you please explain PCA. – Neelam Oct 22 '10 at 13:12
  • @Neelam no problems. PCA = Principal Components Analysis, a data reduction technique: see this excellent tutorial by Lindsay I Smith: http://www.cs.otago.ac.nz/cosc453/student_tutorials/principal_components.pdf – Jeromy Anglim Oct 23 '10 at 02:40
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If you're after a general way to model multiway contingency tables, one powerful approach is to use Poisson regression, often called a log-linear model in this context.

A classic paper on this is Nelder (1974), but there are now more suitable resources for pedagogical purposes freely available online thanks to the generosity of some lecturers or their universities, such as Princeton's Germán Rodríguez: pdf version, html version. There must be less mathematical introductory material out there though?

onestop
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    +1 Log-linear sounds good given the plentiful requirements! :) I'd also recommend Agresti's text on categorical data analysis. – ars Oct 21 '10 at 03:24