Re: imputation of non-independent data

From: jim clark (clark_at_uwinnipeg.ca)
Date: 06/15/04 

Date: Tue, 15 Jun 2004 08:57:28 -0500

Hi

On 15 Jun 2004, Kelly Gallagher wrote:
> I would like to use imputation, given the following scenario:
>
> The data I possess are not independent as they quantify the degree of
> genetic relatedness for PAIRS of individuals sampled from a
> population.
>
> For example:
>
> individual_1 individual_2 relatedness
>
> 1 1 1.00
> 1 2 0.34
> 1 3 0.00
> 1 4 0.79
> 2 2 1.00
> 2 3 ?
> 3 4 0.50
> 4 4 1.00
>
...
> I have tried to use Joe Schafer's NORM software, declaring the
> variables "individual_1" and "individual_2" as dummy variables. In
> doing so, am I using the appropriate model? Alternatively, should I be
> stratifying the
> categorical variables?

I just tried a crude regression approach (perhaps what NORM
does?) and got a result of .66. The SPSS analysis appears below,
although most of stats are not computable because of too few df.
  
data list free / i1 i2 rel.
begin data
    1 1 1.00
     1 2 0.34
     1 3 0.00
     1 4 0.79
     2 2 1.00
     2 3 9
     3 4 0.50
     4 4 1.00
end data.
missing values rel (9).
recode i1 (1 = -3) (2 3 4 = 1) into i1a.
recode i1 (1 = 0) (2 = -2) (3 4 = 1) into i1b.
recode i1 (1 2 = 0) (3 = -1) (4 = 1) into i1c.
recode i2 (1 = -3) (2 3 4 = 1) into i2a.
recode i2 (1 = 0) (2 = -2) (3 4 = 1) into i2b.
recode i2 (1 2 = 0) (3 = -1) (4 = 1) into i2c.
regres /vari = rel i1a to i2c /dep = rel /enter
  /save pred(prd).
  
  
Regression
  
Warnings
 
              
For the final model with dependent variable REL, the
variance-covariance matrix is singular. Influence statistics
cannot be computed.
              
  
Variables Entered/Removed(b)
                                        
 Model Variables Variables Method
       Entered Removed
                                        
 1 I2C, I1C, . Enter
       I2A, I2B,
       I1A, I1B(a)
                                        
¢
a All requested variables entered.
b Dependent Variable: REL
  
Model Summary(b)
 Model R R Square Adjusted R Std. Error
                         Square of the
                                      Estimate
 1 1.000(a) 1.000 1.000 .
                                                   
¢
a Predictors: (Constant), I2C, I1C, I2A, I2B, I1A, I1B
b Dependent Variable: REL
  
ANOVA(b)
 Model Sum of df Mean Square F Sig.
                 Squares
                                                    
 1 Regression .927 6 .155 . .(a)
                                                    
      Residual .000 0 .
                                                    
      Total .927 6
                                                    
¢
a Predictors: (Constant), I2C, I1C, I2A, I2B, I1A, I1B
b Dependent Variable: REL
  
Coefficients(a)
                 Unstandardized Standardized t Sig.
                 Coefficients Coefficients
                                                             
 Model B Std. Error Beta
                                                             
 1 (Constant) .678 .000 . .
      I1A 4.833E-02 .000 .263 . .
      I1B -.233 .000 -.594 . .
      I1C .250 .000 .367 . .
      I2A -.156 .000 -.599 . .
      I2B 1.833E-02 .000 .066 . .
      I2C .395 .000 .760 . .
                                                             
a Dependent Variable: REL
  
Residuals Statistics(a)
              Minimum Maximum Mean Std. N
                                       Deviation
 Predicted .000000 1.000000 .661429 .3931254 7
 Value
 Residual .000000 .000000 .000000 .0000000 7
 Std. -1.682 .861 .000 1.000 7
 Predicted
 Value
 Std. . . . . 0
 Residual
                                                      
a Dependent Variable: REL
  
list i1 i2 rel prd.
  
List
      I1 I2 REL PRD
  1.0000 1.0000 1.0000 1.00000
  1.0000 2.0000 .3400 .34000
  1.0000 3.0000 .0000 .00000
  1.0000 4.0000 .7900 .79000
  2.0000 2.0000 1.0000 1.00000
  2.0000 3.0000 9.0000 .66000
  3.0000 4.0000 .5000 .50000
  4.0000 4.0000 1.0000 1.00000

Best wishes
Jim

============================================================================
James M. Clark (204) 786-9757
Department of Psychology (204) 774-4134 Fax
University of Winnipeg 4L05D
Winnipeg, Manitoba R3B 2E9 clark@uwinnipeg.ca
CANADA http://www.uwinnipeg.ca/~clark
============================================================================