I'm having a look at x-ray waiting times in an emergency department and how these relate to the day of the week and the time of day that requests are ordered. (Want to know if patients have to wait longer for their x-rays on weekends and at night compared with day shifts).

The waiting times have a significant right skew when plotted on a histogram. I divided the continuous variable "waiting times" into 5 categories (0-30 mins being the reference category). I also dummy coded the 6 days of the week and the "time of day" (which was divided into the 3 shifts of the day) into 0-the day in question and 1-the rest of the days of the week.

I performed univariate multinomial regression with waiting times as the dependent variable and each independent dummy variable in turn (omitting Saturday and Night shift from the analysis to act as "reference").

when I entered each variable independently, not one of them showed a significant relationship with x-ray waiting times. On multivariable multinomial regression, I found four variables were demonstrating p values less than 0.05, particularly with the waiting time category of 61-90 mins.

I wondered if anyone knew why this was? If there's a plausible explanation or whether I've made a mistake somewhere? Please help if you have any suggestions as I'm a complete stats amateur ...


You don't really have more than one independent variable. You have multiple levels of a single categorical independent variable. You'll want to read threads like this one and the one linked at the bottom of that page, where the conversation is picked up in more detail. (btw, on that first page, I'd give more weight to @Frank's comment than to my answer.)


In addition to the main question you ask (for which see the thread mentioned by @rolando2), I would not categorize waiting time. You might consider transforming it - for variables that are very skewed to the right, log often works nicely.

But, if you do categorize it as you did, then you don't really have multinomial logistic, you have ordinal logistic

  • $\begingroup$ Not that I'm asking you to quantify this exactly, but how much difference does it make in practice whether one uses ordinal or multinomial? $\endgroup$ – rolando2 Apr 7 '12 at 13:56
  • $\begingroup$ Unfortunately I'm new to stats, so was unsure how to interpret the estimates produced by ordinal logistic as spss doesn't convert them into odds ratios. Any pointers in this direction? $\endgroup$ – Elena love Apr 7 '12 at 21:26
  • $\begingroup$ @rolando I don't think that's answerable in general; you have to take it on a case-by-case basis $\endgroup$ – Peter Flom Apr 8 '12 at 12:06
  • $\begingroup$ @Elenalove If you use SAS, see a paper I wrote $\endgroup$ – Peter Flom Apr 8 '12 at 12:08
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    $\begingroup$ The statement "you don't really have multinomial logistic, you have ordinal logistic" doesn't make sense. The ordinal logistic model is a submodel of the multinomial logistic. What you've said is like saying "You don't have a polygon, you have a square". $\endgroup$ – Macro Apr 9 '12 at 22:33

First, I want to say that this is a classic Survival Analysis situation. It's called by different names in different disciplines; while SA is most common, 'Time to Event Analysis' may be more intuitive in your situation. SA can be done in SPSS, although it's been a while since I've had access to SPSS, so I can't advise on the mechanics of performing the analysis, unfortunately. Googling SA SPSS yielded this pdf, which looks like it may be helpful in that regard. I would recommend you use a Cox Proportional Hazard model for this analysis, as you are primarily interested in the effect of your covariates, rather than the baseline hazard rate. These things having been said, I should acknowledge that if a transformation (such as taking the log) sufficiently normalizes your response variable, multiple linear regression should be acceptable. If you are totally unfamiliar with SA, are unlikely to have to work with similar situations in the future, and/or are not in a position to pick up new techniques right now, the costs of trying to learn about SA would outweigh the benefits, and multiple regression would probably be your best bet.

Like others here, I'm generally against categorizing variables. (If you just wanted to know about this as background information, you could read this question and answer where I discuss related issues.) However, running a SA or a multiple regression with an appropriate transform will take care of your issue with your response variable, and I have no qualms with grouping your covariates in this case, given your substantive question. I would create dummies for weekend (i.e., 0 for weekdays & 1 for weekend days), and shift (0 would be the default day shift against which you want to compare, and then one new column / variable for 2nd shift & another new column / variable for 3rd shift). I might also add interaction terms (2 new columns as the products of weekend multiplied by evening shift and by night shift) as I suspect this may be of interest for you. (Specifically, the question might be, 'if nights & weekends are slower, would, say, Sunday night be even slower than I might otherwise suspect given that it's both a weekend and an overnight'?) You could always keep all your days coded, but it doesn't sound like you are intrinsically interested in Tuesday vs. Wednesday per se, just weekday vs. weekend, and this route should give you more statistical power with which to detect an effect that was actually there.

As to your original question regarding why something might be significant when more predictor variables are entered into the model, this has to do with how significance testing works. In multiple regression, you are comparing the slope you found to a null distribution that is estimated using the residual variability. As you enter more covariates into the model, the residual variability decreases. (The residual degrees of freedom also decreases, so it's possible that you could loose power, but more likely you will gain power.)

I would recommend you fit a model with all of the above dummies, and then interpret the results rather than focusing on whether individual covariates are 'significant'. I would also typically advise against running lots of univariate models. Good luck with your project.

  • $\begingroup$ The survival analysis suggestion is intriguing, but it would require a lot of data restructuring and I don't see the payoff. Linear regression with a transformed outcome variable, or ordinal logistic regression as Peter mentioned, looks pretty adequate for answering the research questions and seems more manageable, given that the questioner wrote, "I'm a complete stats amateur...." $\endgroup$ – rolando2 Apr 8 '12 at 20:01
  • $\begingroup$ @rolando2, you raise a good point. There is a tradeoff here, because SA is more advanced & may require learning new material, however, it is the appropriate analysis in this situation. I suspect it wouldn't be too difficult (although I may be wrong). If the OP has to deal w/ situations like this in the future, there may well be a payoff. In then end, the OP will have to make a decision about which way to go. $\endgroup$ – gung - Reinstate Monica Apr 8 '12 at 20:13
  • $\begingroup$ I think it will only make a big difference if there is censoring. That's the main problem that SA deals with. But I am all for people learning more, or, if appropriate, hiring consultants who know more. $\endgroup$ – Peter Flom Apr 8 '12 at 21:01
  • $\begingroup$ @PeterFlom, you're right. AFAIK, if there's no censoring (which appears to be the case here) & a transformation (such as the log, which you appropriately suggest) generates sufficiently normal data, then OLS could be used w/o harm. This is where my philosophical orientation comes out: Using OLS to model survival times leads us to think about the data in a sub-optimal way, & for me, thinking about the data is the point. $\endgroup$ – gung - Reinstate Monica Apr 8 '12 at 21:11
  • $\begingroup$ Well @gung, there's suboptimal and there's just plain wrong. Optimal usually means a lot of work with an expert. So, here on CV I try to just make sure people aren't just plain wrong. :-). But thinking about the data is the main thing. You're absolutely right about that. Unfortunately, thinking about the data is not encouraged in a lot of stats courses in substantive areas. $\endgroup$ – Peter Flom Apr 8 '12 at 23:00

If you want to learn the difference in mean wait time, comparing weekends/nights to day shifts, regress the wait times on a dummy variable for weekends/nights (1 for weekends/nights, 0 for day shifts). The coefficient for the dummy variable estimates the difference that's of interest.


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