Multivariate Statistics

Often in experimental design, multiple variables are related in such a way that by analyzing them simultaneously additional information, and often times essentially information, can be gathered that would be missed if each variable was examined individually (as is the case in univariate analyses). For example, in univariate statistics, we study random variables that have a normal distribution (characterized by the usual bell-shaped curve), while in multivariate statistics we study groups of random variables that have a multivariate normal distribution. Such variables are related in a way that the effects can’t be meaningfully interpreted separately.

Topics

References

Penn State University (2013) STAT 505: Applied multivariate statistical analysis (course notes)
https://online.stat.psu.edu/stat505/lesson/7

Rencher, A.C. (2002) Methods of multivariate analysis (2nd Ed). Wiley-Interscience, New York.
https://www.ipen.br/biblioteca/slr/cel/0241

Johnson, R. A. and Wichern, D. W. (2007) Applied multivariate statistical analysis. 6th Ed. Pearson.
https://www.webpages.uidaho.edu/~stevel/519/Applied%20Multivariate%20Statistical%20Analysis%20by%20Johnson%20and%20Wichern.pdf

Pituch, K. A. and Stevens, J. P. (2016) Applied multivariate statistical analysis for the social sciences. Routledge.

13 thoughts on “Multivariate Statistics”

  1. Dear Charles,
    I wanted to ask you if you know about forecast methods for multivariate time series.
    The methods in this section “Multivariate Statistics” are all rather to analyze and simplify multivariate data, right?
    Our goal is to forecast time series with several variables.
    Thank you very much and best regards,
    Janne

    Reply

  2. Dr. Zaiontz good morning, Dr. how can I develop a confirmatory factor analysis CFA?
    Could you please give me a suggestion?

    Thank you

    Dr. Zaiontz buenos días, Dr. como puedo desarrollar un análisis factorial confirmatorio?
    Podría por favor regalarme una sugerencia?
    Muchas gracias

    Reply

  3. Hi Charles, I feel honoured to have a discussion with you. Kindly help me with this : I want to test efffects of 13 factors (divided into 31 sub-factors questionnaire survey i.e answers to 31 questions will produce score of 13 factors to relate to 03 result factors) on 03 factors (again divided into five sub-factors). For example, how 13 habits can improve 03 results (say mind, body and soul)! Now 13 habits (factors) converted to 31 questions whose answers will give the score on 03 results(factors) which are subdivided into five sub-factors (Say, mind – smile, memory; body- strength, muscles ;soul-peacefulness.). Pl guide me how do I proceed with data collected and what all Statistical analysis tools I must use to complete my work. Regards

    Reply

      • So kind of you, Charles. I plan to test 13 Hypotheses that state 13 habits can improve 05 results as mentioned above. But that way I will have to formulate 13X5=65 hypotheses. this will be a voluminous task. Is there any way to reduce the work involved in this so that I can test the factors responsible for the results?Also, I want to know what should be the pattern of my questionnaire..my respondents (sample for pilot test & population) are professionals in the related field, so content validity can also be ensured by the questionnaire.

        Reply

        • let me elaborate a bit more on this. First hypothesis is “Good habits improve good health”. Good habits are ensured by 13 factors and good health defined by 03 factors. 13 factors subdivided and covered through 31 questions and 03 factors covered though 05 sub-factors.

          Reply

        • Sorry Sanjay, but we would need to get into a lot more detail before I could offer much advice, and I frankly don’t have the time to do this now, especially since I plan to go on vacation tomorrow.
          Charles

          Reply

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