Solved – Data analysis with only dumthe variables

binary datacategorical datalogisticregression

I would like to find out whether there is a significant relationship between No-show rates and the part of the week (weekday/weekend), this in order to be able to suggest whether restaurants should allow or not allow reservations on certain days of the week.

Am I right to think a logistic regression would be suitable for this? As you can see from the preview of my data I only have dummy variables available, and one continuous, which is making me confused about which type of regressions are possible. Or should I not use a regression at all? My main confusion I think lies in that I do not know what the outcome of my analysis should be, a yes/no answer, a p-value, i don't know 🙁

Best Answer

From your question, it sounds like this is your main issue:

...in order to be able to suggest whether restaurants should allow or not allow reservations on certain days of the week.

To address this question, you'll want to restrict your analyses to just the people who made a reservation (folks who come in without a reservation don't contribute to your understanding of whether no-shows are more likely on certain days). You're right that you can use logistic regression for this, with whether or not the reservation no-showed (0 or 1) as the outcome (or perhaps cancellations or no-shows, as per Matt Barstead's comment), and whether or not it's a weekend and size of the reservation as predictors. I also recommend you include an interaction between weekend and size, to test whether the relationship between size of reservation and likelihood of a no-show is different on weekends vs. weekdays (or whether smaller vs. larger parties have a bigger difference between weekend and weekday no-show rates, depending on how you look at it). As always, plotting your results will make interpretation easier. Here's a relevant tutorial I wrote up a couple years ago: https://blogs.uoregon.edu/rclub/2016/04/05/plotting-your-logistic-regression-models/

If you want to examine the relationship between no-showing and weekend separately from the relationship between no-showing and reservation size, you can run two separate logistic regression models. Alternatively, you can run the no-showing and weekend model as a cross-tab analysis, if you prefer, possibly using Fisher's exact test to test the hypothesis that weekend and no-showing are unrelated.

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Solved – Dumthe variable trap issues

You should get the "same" estimates no matter which variable you omit; the coefficients may be different, but the estimates of particular quantities or expectations should be the same across all the models.

In a simple case, let $x_i=1$ for men and 0 for women. Then, we have the model: $$\begin{align*} E[y_i \mid x_i] &= x_iE[y_i \mid x_i = 1] + (1 - x_i)E[y_i \mid x_i = 0] \\ &= E[y_i \mid x_i=0] + \left[E[y_i \mid x_i= 1] - E[y_i \mid x_i=0]\right]x_i \\ &= \beta_0 + \beta_1 x_i. \end{align*}$$ Now, let $z_i=1$ for women. Then $$\begin{align*} E[y_i \mid z_i] &= z_iE[y_i \mid z_i = 1] + (1 - z_i)E[y_i \mid z_i = 0] \\ &= E[y_i \mid z_i=0] + \left[E[y_i \mid z_i= 1] - E[y_i \mid z_i=0]\right]z_i \\ &= \gamma_0 + \gamma_1 z_i . \end{align*}$$ The expected value of $y$ for women is $\beta_0$ and also $\gamma_0 + \gamma_1$. For men, it is $\beta_0 + \beta_1$ and $\gamma_0$.

These results show how the coefficients from the two models are related. For example, $\beta_1 = -\gamma_1$. A similar exercise using your data should show that the "different" coefficients that you get are just sums and differences of one another.

Solved – SPSS dumthe variables in OLS

If you have the advanced statistics package that allows you do estimate generalized linear models (see the menus Analyze -> Generalized Linear Models or the GENLIN command), you can have SPSS on the fly generate the dummy variables. Given your data it may be good to see if some of the newer mixed model commands can estimate auto-regressive components for panel data.

Alternatively, you can use the DO REPEAT syntax to efficiently generate your dummy variables for use in regression equations. For instance, for your weekDay variable it would be;

VECTOR weekDay_Dummy(7,F1.0).
DO REPEAT weekDay_Dummy = weekDay_Dummy1 to weekDay_Dummy7 /i = 1 to 7.
    DO IF weekDay = i. 
        COMPUTE weekDay_Dummy = 1.
    ELSE IF weekDay <> i.
        COMPUTE weekDay_Dummy = 0.
    END IF.
END REPEAT.

As long as your variables are in a sequential list of integer values, the do repeat command will work (if they aren't in a sequential list see the AUTORECODE command). Then in the linear regression command you can subsequently use the TO operator to specify a list of variables that are in sequential order in your dataset (extra note it has to do with the order of the variables in the dataset, nothing to do with the names directly).

Below I have an example.

data list free / company  sector  obsDay weekDay  stockPrice.
begin data
1        15      1      3        10.40
1        15      2      4         9.42
1        15      3      5         9.66
1        15      4      1        11.00
1        15      5      2        10.21
2        10      1      3        43.55
2        10      2      4        43.50
2        10      3      5        40.31
2        10      4      1        48.43
2        10      5      2        43.00
3        20      1      3        10.00
3        20      2      4        11.00
3        20      3      5        12.00
3        20      4      1        13.00
3        20      5      2        14.00
end data.
dataset name examp.

VECTOR weekDay_Dummy(7,F1.0).
DO REPEAT weekDay_Dummy = weekDay_Dummy1 to weekDay_Dummy7 /i = 1 to 7.
    DO IF weekDay = i. 
        COMPUTE weekDay_Dummy = 1.
    ELSE IF weekDay <> i.
        COMPUTE weekDay_Dummy = 0.
    END IF.
END REPEAT.

REGRESSION
  /MISSING LISTWISE
  /STATISTICS COEFF OUTS R ANOVA
  /CRITERIA=PIN(.05) POUT(.10)
  /NOORIGIN 
  /DEPENDENT stockPrice
  /METHOD=ENTER weekDay_Dummy2 to weekDay_Dummy5.

Another extension command with more flexibility for writing dummy variables, SPSSINC_CREATE_DUMMIES (written in Python) is on the developerworks site (but I have not used it). Also one of the members here, ttnphns, has some tools to accomplish similar tasks on his site. Given your example though a few do repeat commands should be sufficient.

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Solved – Dumthe variable trap issues

Solved – SPSS dumthe variables in OLS

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