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So I am running a Least Squares Dummy Variable Regression (LSDV1) involving data from 21 states observed 3 times (2007, 2008, 2009) and dropping one of the dummy value states. I have 8 independent variables that I am seeking to use (ENTER method).

When I regress I find two strange things: 1) 7 of the 8 independent variables are excluded 2) 1 of my 20 states (21 - 1 dummy dropped) is excluded, too

Huh

UPDATE: Changed IV to independent variable

LOGS

Model Summary               
Model   R   R Square    Adjusted R Square   Std. Error of the Estimate
1   .883a   .780    .676    .07702


ANOVAa                      
Model       Sum of Squares  df  Mean Square F   Sig.
1   Regression  .886    20  .044    7.466   .000b
    Residual    .249    42  .006        
    Total   1.135   62          

Coefficientsa                               
Model       Unstandardized Coefficients     Standardized Coefficients   t   Sig.    Collinearity Statistics 
        B   Std. Error  Beta            Tolerance   VIF
1   (Constant)  .854    .080        10.694  .000        
    EducationandTrainingActivities  .024    .021    .202    1.126   .267    .162    6.180
    StateIsAlaska   .024    .076    .039    .322    .749    .363    2.751
    StateIsArizona  .109    .055    .173    1.971   .055    .675    1.481
    StateIsArkansas -.333   .063    -.529   -5.302  .000    .525    1.905
    StateIsCalifornia   -.108   .055    -.172   -1.956  .057    .675    1.481
    StateIsDelaware -.307   .055    -.487   -5.532  .000    .675    1.481
    StateIsFlorida  -.063   .055    -.101   -1.144  .259    .675    1.481
    StateIsIdaho    .060    .063    .095    .950    .347    .525    1.905
    StateIsIllinois .049    .055    .078    .890    .379    .675    1.481
    StateIsIndiana  .061    .063    .097    .967    .339    .525    1.905
    StateIsKansas   .045    .063    .071    .715    .479    .525    1.905
    StateIsKentucky .019    .063    .030    .300    .765    .525    1.905
    StateIsMichigan .080    .055    .127    1.440   .157    .675    1.481
    StateIsMissouri -.031   .055    -.049   -.561   .578    .675    1.481
    StateIsNewJersey    .115    .063    .182    1.823   .075    .525    1.905
    StateIsNorthCarolina    .043    .055    .068    .772    .444    .675    1.481
    StateIsUtah .047    .076    .075    .626    .535    .363    2.751
    StateIsVermont  .107    .055    .170    1.932   .060    .675    1.481
    StateIsVirginia .020    .076    .032    .266    .791    .363    2.751
    StateIsWashington   .083    .055    .132    1.495   .142    .675    1.481


Excluded Variablesa                     
Model       Beta In t   Sig.    Partial Correlation Collinearity Statistics
                        Tolerance
1   ManagementActivities    .b  .   .   .   .000
    PersonnelServices   .b  .   .   .   .000
    PlanningandResearchActivities   .b  .   .   .   .000
    InformationSystemActivities .b  .   .   .   .000
    SupportServices .b  .   .   .   .000
    FinanceandBudgetActivities  .b  .   .   .   .000
    PublicInformationandLiaisonActivities   .b  .   .   .   .000
    StateIsTexas    .b  .   .   .   .000
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  • $\begingroup$ This is because of perfect multi collinearity. When you use dummy variable you should always exclude one of the categories. Example in your case, if you have 21 states you need to specify only 20 dummy's and the 21st dummy would be your reference dummy. Please consult any standard regression textbooks or the following website ats.ucla.edu/stat/mult_pkg/faq/general/dummy.htm $\endgroup$
    – forecaster
    Commented Feb 21, 2014 at 17:53
  • $\begingroup$ I did exclude the dummy "1 of my 20 states (21 - 1 dummy dropped) ") $\endgroup$
    – user39799
    Commented Feb 21, 2014 at 17:56
  • $\begingroup$ Are you using SPSS? Can it not just be that 7 out of 8 independent variables are found not significant and therefore dropped out of the model? $\endgroup$
    – Kasper
    Commented Feb 21, 2014 at 18:05
  • $\begingroup$ Could you share the data and the program, without which it is immpossible to answer this question. $\endgroup$
    – forecaster
    Commented Feb 21, 2014 at 18:05
  • $\begingroup$ Yes, I'm using SPSS. But I'm using ENTER, not STEPWISE or BACKWARD. I should be getting all of them, even if not significant, in the model (yes?). $\endgroup$
    – user39799
    Commented Feb 21, 2014 at 18:07

2 Answers 2

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Imagine this: a binary variable called male where males are coded as 1 and females are coded as 0 is used to predict an outcome, say, income:

$income = \beta_0 + \beta_1 male$

The $\beta_1$ is sufficient to tell the mean income difference between the two sexes. Now, we introduce another predictor female which codes females as 1 and males as 0:

$income = \beta_0 + \beta_1 male + \beta_2 female$

What would happen? The software will force either male or female out. Because by know who is not a male, we will know who is a female.

Your situation is the similar. Texas got excluded becuase by knowing a state not being any of the other 20 states, then we will know that it's Texas. To the model it is redundant information, and hence excluded.

What about the other seven being excluded? My guess is that your research design may have some problem, capturing all these non-state variables that are strongly associated with or affected by state identity. For instance, if your unit of analysis is different state offices, even you can have multiple offices sampled in Idaho, you can still end up having all the offices providing saying yes to PersonnelService, because it's a state policy to have it.

Now, suppose Idaho and California both mandate PersonnelService, then the binary variables have the following relationship:

$PersonnelService = StateIsCalifornia + StateIsIdaho$

This will cause a perfect collinearity in regression model. Either one of them can be thrown out, and it turned out PersonnelService got excluded.

The solution to your problem and go back to square one and really examine if those features are really dictated by states. In the same state, do they either score all 1 or all 0. If so, the model you present here will not work.

You'd have to either aggregate the states into a large areas like region, or go back to find some other indicators from the unit of analysis that is not a constant within each state.

Another side comment, you only have 63 cases. Which is unrealistically low to fit a model with 25+ predictors. If the data collection is already a done deal, I'd discuss with the team and consider giving up all the states: if you have 3 samples for each state, and then further slicing them up by 8 different indicator... the model is likely to be bad.

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  • $\begingroup$ OK, the features are dictated by states, specifically by statute. Not every state legislature enacted the same laws when it came to these issues. The independent variables are scaled scores for each area, so for your example California's laws gives some power over PersonnelServices to the state and others the locality, a 2 on a 1-3 scale. Texas, on the other hand, gave effectively nothing (1 on the 1-3 scale). Now, since laws rarely change, over the course of my data collection (2007, 2008, 2009) these scores are static; they never changed. $\endgroup$
    – user39799
    Commented Feb 21, 2014 at 19:18
  • $\begingroup$ I see. Though given the low sample size. I would suggest tabulation by state rather than any regression. $\endgroup$
    – Penguin_Knight
    Commented Feb 21, 2014 at 19:29
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Solved my problem: ran regression against years, not states. Dropped 1 dummy year and everything now works. Thanks!

Model Summary                                
Model        R       R Square        Adjusted R Square       Std. Error of the Estimate
1        .518a       .269        .128        .12635

ANOVAa                                               
Model                Sum of Squares      df      Mean Square         F       Sig.
1        Regression      .305        10      .030        1.910       .065b
         Residual        .830        52      .016                
         Total       1.135       62                      


Coefficientsa                                                                
Model                Unstandardized Coefficients                 Standardized     Coefficients       t       Sig.        Collinearity Statistics         
             B       Std. Error      Beta                        Tolerance       VIF
1        (Constant)      .731        .114                6.390       .000                
     ManagementActivities        .034        .015        .350        2.256       .028        .583        1.715
     PersonnelServices       -.007       .051        -.029       -.131       .896        .281        3.557
     PlanningandResearchActivities       -.053       .024        -.597       -2.181      .034        .188        5.331
     InformationSystemActivities         -.021       .018        -.210       -1.134      .262        .411        2.433
     SupportServices         -.022       .010        -.554       -2.121      .039        .206        4.847
     FinanceandBudgetActivities      .054        .021        .743        2.626       .011        .176        5.693
     EducationandTrainingActivities      -.024       .021        -.204       -1.127      .265        .428        2.339
     PublicInformationandLiaisonActivities       .113        .034        .972        3.386       .001        .171        5.865
     Yearis2007      .014        .039        .047        .347        .730        .750        1.333
     Yearis2009      .030        .039        .104        .758        .452        .750        1.333
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