Regression analysis with discrete dependent variable and continuous independent var.

[blindfreak]

Using MiniTab, I calculated Spearman's rho and Pearson's r (you find the "How to" in Minitab support ID1198). I ran it with all my data sets and found both (rho and r) to be very similar. As Spearman's analysis only assumes a monotonic dependence, while Pearson's assumes a linear dependence I would conclude, that a linear model could be used (right?).
This is further supported by the fact, that both (rho and r) gave the same directional results as a linear regession model.
While Spearman's analysis only allows to analyse a single factor at a time, based on the findings described above, could I still apply a multifactorial linear regression model?

Again, many thanks!!!
Linus

[Barbara B]

Imho ordinal logistic regression is the correct approach if your response is a ranked variable (with or without non-equidistant ratings). Ordinal data is defined as a variable which has a ranking, but the distance between the ranks couldn't be quantified and aren't equal. On the Minitab help pages you'll find the following

Use ordinal logistic regression to perform logistic regression on an ordinal response variable. Ordinal variables are categorical variables that have three or more possible levels with a natural ordering, such as strongly disagree, disagree, neutral, agree, and strongly agree.

An ordinal regression analyzes which predictor has an effect on the ranking, e. g. if the amount of revenue has an impact on the students' attractivity ranking. Due to the 71 different ranks you got 70 different coefficients (1 level is used as reference level and 70 differences are calculated for the other 70 ranks) along with a test if this coefficient is different from the reference level (in this case p<0.05 if alpha=5%).

But the use of 71 different rankings will blur the results, so I would try to group the rankings, e. g.

• 1 - most attractive: rank 1-5
• 2 - very attractive: rank 6-10
• 3 - attractive: rank 11-20
• 4 - less atttractive: rank 21-30
• 5 - unattractive: rank 31-71

Barbara

[Miner]

In Reply to Parent Post by blindfreak

Using MiniTab, I calculated Spearman's rho and Pearson's r (you find the "How to" in Minitab support ID1198).

Since you found this, I searched and discovered that Minitab has a hidden, experimental command for Rank Regression called RREGRESS (Minitab support ID 619). You cannot access it through the menu, but must enter it on the command line (Editor > Enable Commands).

[blindfreak]

@Miner: Wow! Amazing that you found that hidden command! Many thanks for your efforts!

I conducted the rank regression and got the following output:

Rank Regression: Ideal Employ versus ENVTL. IMPAC; ENVTL. MGMT.; ...
The regression equation is
Ideal Employer Rank = 31,1 + 0,0850 ENVTL. IMPACT - 0,201 ENVTL. MGMT. +
0,149 DISCLOSURE + 0,000009 Revenue $ mio - 0,000171 Profit $ mio
　
Coefficient Coefficient
Predictor Rank Least-sq Rank Least-sq
Constant 31,05 29,33 18,86 17,22
ENVTL. IMPACT 0,0850 0,1112 0,1990 0,1817
ENVTL. MGMT. -0,2007 -0,1842 0,2351 0,2147
DISCLOSURE 0,1492 0,1385 0,1426 0,1302
Revenue $ mio 0,00000922 0,00000836 0,00004042 0,00003692
Profit $ mio -0,0001714 -0,0001511 0,0005948 0,0005433
Hodges-Lehmann estimate of tau = 18,19 Least-squares S = %2
　
Unusual observations
Ideal
ENVTL. Employer
Observation IMPACT Rank Pseudo Fit SE Fit Residual
23 45,3 29,00 28,24 38,42 11,86 -9,42 X
51 48,4 44,00 45,79 40,13 11,05 3,87 X
59 63,8 50,00 51,78 32,56 12,56 17,44 X
X denotes an observation whose X value gives it large leverage.

My question: Is there any number or value that assesses the strength or confidence of the relationship (I am desperately looking for something like a p-value or adjusted R-square value)? In the end, I want to reject my H0 hypothesis and need the relevant information to accomplish that.

@ Barbara B: Thanks for the 'grouping hint'! I will definitiely try that approach. Many thanks for your efforts as well!

[Miner]

The Hodges-Lehmann estimate of tau is the number that you want. I am researching information on how to interpret it, but I can tell you that the lower this number is, the better.

The third number from the left in the coefficients table is the equivalent of the SE (standard error) in a least squares analysis. Again, the smaller the better.

[blindfreak]

For your information:
I opened a new thread on the Hodges-Lehmann question because it is quite deviant from my original question.