I have a big dataset (n>5,000) on corporate indebtedness and want to test wether SECTOR and FAMILY-OWNED are significant to explain it. The information is in percentage (total liabilities/total assets) but is NOT bounded: many companies have an indebtedness above 100%. My hypothesis are that SERVICES sector is more indebted than other sectors, and FAMILY-OWNED companies are less indebted than other companies.
If the data were normally distributed and had equal variances, I'd perform a two-way ANOVA.
If the data were normally distributed but were heteroscedastic, I'd perform a two-way robust ANOVA (using the R package "WRS2")
As the data is not normally distributed nor heteroscedastic (according to many tests I performed), and there is no such thing as a "two-way-kruskall wallis test", which is the best option?
1) perform a generalized least squares regression (therefore corrected for heteroscedasticity) to check for the effect of two factors in my dependent variable?
2) perform a non-parametric ANCOVA (with the R package "sm"? Or "fANCOVA"?)
What are the pros and cons of each alternative?
Start with the properties of the DV and Google search on the query what regression should I use. Then match your DV to the appropriate method and go from there. Best wishes David Booth
Often, the log-normal distribution is a sensible assumption for percentages that are not bounded at 100%. Are there any arguments against this in your case?
It makes a huge difference for interactions if you analyze the data on the original scale or on the log scale. If is is sensible to assume relative effects (a given impulse will change the response depending on the "base value" of the response, so absolute changes will differ when the base values differ), interactions seen on the original scale are highly misleading in terms of the functional interpretation (i.e. when you aim to understand the interplay of the factors).
Jochen Wilheim, thank you for your answer. No, there are no arguments against transforming my variable into log(indebtedness). Except, maybe, for the interpretation of the results (=of the effects of sector and familly-owned).
Would you say that it is best to transform into log-normal and perform a two-way anova, or two-way robust anova, instead of a generalized least squares regression?
A few comments:
- The traditional "two-way Kruskal-Wallis test" is the Scheirer–Ray–Hare test. However, I have found that this test sometimes fails to find a significant interaction when other procedures will.
- An applicable nonparametric approach is Aligned Ranks Transformation Anova. The R implementation is easy to use, and allows for post-hoc tests. With the caveat that I wrote it, see: https://rcompanion.org/handbook/F_16.html .
- If the only issue with a traditional OLS anova is heteroscedasticity, in R you might use the white.adjust option in the Anova() function in the car package to account for this. ... Based on your description, I don't know if the non-normality will be a problem for traditional anova in your case.
- With n > 5000, a hypothesis test is like to return significant results even for small effect sizes. Be sure to not rely on p-values too much, and to assess the size of the effects, and the practical importance of the effects you discover.
Thank you very much for your detailed answer, Salvatore S. Mangiafico ! My two way anova (not robust for heteroscedasticity) gave me the results I expected, but I was afraid due to non normality, heteroscedasticity and unbalanced data. I will try with the white.adjust option and type III anova.
At first, i thought about using OLS. However, due to the fact that the distribution of each sector's indebtedness is different (and definitely non normal), i thought about GLS. Maybe this is the best option if I test three factors?
Luiza Betina Petroll Rodrigues , the aligned ranks approach can handle multiple factors with the caveat that you also have to include all interactions in the model. ... You might run the OLS or GLS model and post a histogram or q-q plot of the residuals of the analysis. With such a large sample size, the non-normality of the data may not be a problem anyway. ... That being said, Gamma regression may be appropriate for your data. Wikipedia has a usable introduction to the Gamma distribution: https://en.wikipedia.org/wiki/Gamma_distribution . I believe the dependent variable cannot take on the value zero (or less than zero).
JFTHOI. Jochen Wilhelm's answer was the most complete correct answer. You cannot use.least squares for your DV which is a percentage. I believe that Rosner Fundamentals of Biostatistics is one source that covers this. . ALWAYS DESCRIBE THE DV WHICH IS HOW YOU DECIDE TYPE OF REGRESSION. Best wishes David Booth
- Badges
- Science method
- Similar topics
- Mathematics
- Statistics
- Statistical Modeling
- Analyses of Variance
- ANOVA