I am doing my dissertation on electrical smart meters design. I am questioning whether the design of the features is limiting the potential Reduced Household Energy Consumption (RHHEC) as currently, smart meters are underperforming in terms of RHHEC when compared to predictions.
I have data on energy reduction status binary Yes/No and a 5-point Likert scale from a large decrease to a large increase in energy consumption. I also have data on 12 different smart meter features concerning:
I have supplemented these questions with comment boxes to collect information on what makes an easy to find and use a feature and what households valued in a useful feature
What I want to do is compare this information between those households that saw RHHEC and those who did not to look for trends e.g. households who find the features hard to use or cannot find a certain do not see RHHEC
How would I go about analysing these?
I have considered a chi-square, linear regression or 2 samples t-test, can I perform multivariate analysis on all 12 features at once compared to RHHEC status (Y/N) or should I assess each feature individually?
Following this can I perform PCA or use dendrograms or is a simple scatterplot matrix the best?
Hi, Callum:
Here is an analysis methodology which is perfect for your application. I provide links to free articles: the reference sections of these articles typically cite pay-for-view articles—if you prefer.
The methodology derives from the “optimal data analysis” (ODA) paradigm—the only methodology which specifically maximizes predictive accuracy:
- https://odajournal.com/2017/04/18/what-is-optimal-data-analysis
- https://odajournal.com/2014/04/06/a-statistical-guide-for-the-ethically-perplexed-chapter-4-panter-sterba-handbook-of-ethics-in-quantitative-methodology-routledge-2011-clarifying-disorientation-regarding/
Specifically, the analytic method is called “classification tree analysis” (CTA), and there are three variations. In your application, for all variations of CTA:
- The class ("dependent") variable is whether (e.g., coded as 1) or not (e.g., coded as 0) the household (each household is an "observation" in the data set) watched RHHEC.
- All of the other Likert and binary (and multicategorical--if there are any) variables which you mention are treated as attributes ("independent" variables).
The initial algorithm is known as hierarchically optimal CTA, or HO-CTA:
- https://odajournal.com/2015/05/11/obtaining-a-hierarchically-optimal-cta-model-via-unioda-software/
The second-generation methodology is known as enumerated optimal CTA, or EO-CTA:
- https://odajournal.com/2015/05/14/obtaining-an-enumerated-cta-model-via-automated-cta-software-2/
And, the current version—fundamental to “novometric” (Latin: new measurement) theory—finds every statistically viable optimal model which exists for your sample.
- https://odajournal.com/2016/07/12/how-many-eo-cta-models-exist-in-my-sample-and-which-is-the-best-model/
If you or others are interested, there are hundreds of related articles in the free eJournal, https://ODAJournal.com
I am not familiar with Prof. Paul Yarnold 's approach so I would suggest a possible alternative, assuming that your DVs are of binary (yes,No) type: logistic regression. I am attaching a set of class notes by Prof. Frank Harrell that includes examples. This procedure should be available in any Statistical Computer package you may have. Best wishes, David Booth
Dear Raaed Fadhil :
Yes, indeed, discriminant analysis. :-)
If you purposively suggested "discernment"--which has a different (non-statistical) meaning--that also satisfies (and to some extent, fits) the acronym, and I apologize for my misunderstanding.
Be that as it may, in the early days of discovery of maximum-accuracy methods, the acronym “ODA” was in fact used to indicate optimal discriminant analysis!
- Soltysik, R.C., & Yarnold, P.R. (1991). MAKE45: A user interface for multivariable optimal discriminant analysis via SAS/OR. Applied Psychological Measurement, 15, 170.
- Soltysik, R.C., & Yarnold, P.R. (1994). Univariable optimal discriminant analysis: One-tailed hypotheses. Educational and Psychological Measurement, 54, 646-653.
- Yarnold, P.R., Soltysik, R.C., & Martin, G.J. (1994). Heart rate variability and susceptibility for sudden cardiac death: An example of multivariable optimal discriminant analysis. Statistics in Medicine, 13, 1015-1021.
- Soltysik, R.C., & Yarnold, P.R. (1994). The Warmack-Gonzalez algorithm for linear two-category multivariable optimal discriminant analysis. Computers and Operations Research, 21, 735-745.
- Ostrander, R., Weinfurt, K.P., Yarnold, P.R., & August, G. (1998). Diagnosing attention deficit disorders using the BASC and the CBCL: Test and construct validity analyses using optimal discriminant classification trees. Journal of Consulting and Clinical Psychology, 66, 660-672.
- Soltysik, R.C., & Yarnold, P.R. (1998). Unit-weight MultiODA: Maximum accuracy discriminant analysis with unit-valued attribute coefficients. Applied Psychological Measurement, 22, 394.
Many other examples of this usage of the ODA acronym by a host of laboratories other than mine can be found in the Publications Tab of the ODA eJournal-- https://ODAJournal.com
However, the “D” in the acronym soon became used to refer to “Data” because (a) the algorithm could handle most any data configuration and thus was NOT limited to problems typically analyzed via legacy discriminant analysis methods, and (b) the algorithm does, in fact, optimize (maximize) the classification accuracy of legacy discriminant analysis.
- Yarnold, P.R., & Soltysik, R.C. (1991). Refining two-group multivariable classification models using univariate optimal discriminant analysis. Decision Sciences, 22, 1158-1164.
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