*! version 1.1.1 24jan2017

Title

mkonfound -- Beta version: For multiple studies, this command calculates (1) % bias necessary to invalidate/sustain an inference; (2) the impact threshold of an omitted confounding variable to invalidate/sustain an inference.

Syntax

mkonfound
[]
[, options]

Main
var1 the observed t-ratio from each study

var2 the degrees of freedom from each study

Description

mkonfound calculates the impact of an omitted variable necessary to invalidate an inference of a
regression coefficient for multiple studies. The command also assesses how strong an omitted
variable must be correlated with the outcome and with the predictor of interest to invalidate/sustain the
inference for each study. Users input two variables: the observed t-ratio and the degrees of freedom for each study.
The command mkonfound produces four variables. The first variable is itcv_, indicating the
impact of an omitted variable needed to invalidate/sustain the inference. The second variable is
r_cv_y, indicating the correlation between the omitted variable and the outcome necessary to
invalidate/sustain an inference, conditioning on other covariates. Third variable is r_cv_x,
indicating the correlation between the omitted variable and the predictor of interest necessary
to invalidate/sustain an inference, conditioning on other covariates. Fourth variable is
stat_sig_, indicating if the original regression coefficient is statistically significant;
1 if yes and 0 otherwise.

mkonfound also calculates how much bias there must be in an estimate to invalidate (or to sustain) an
inference for multiple studies. The % bias necessary to invalidate/sustain an inference is interpreted
in terms of sample replacement. Users input two variables: the observed t-ratio and the degrees
of freedom in each study. The command mkonfound produces two variables. The first variable is
percent_replace, indicating what % of the original cases must be replaced to invalidate the
inference; the second variable is percent_sustain, indicating what % of the original cases
must be replaced to sustain an inference.

Options

sig(#) Significance level of the test; default is 0.05 sig(.05). To change the significance level to .10 use sig(.1)

nu(#) The null hypothesis against which to test the estimate. Null hypothesis is defined as a correlation, ranging from -1 to 1. The
default is 0 nu(0)

onetail(#) One-tail or two-tail test;
the default is two-tail onetail(0);
to change to one-tail use onetail(1)

rep_0(#) For % bias, this controls the effect in the replacement cases;
the default is the null effect (which may or may not be 0) rep_0(0); to force replacing cases with effect of zero use rep_0(1)

z_tran(#) Calculates the % bias based on Fisher's z-transformation (only apply to non-zero hypothesis testing);
default calculation is based on the original test statistic z_tran(0);
to calculate based on Fisher's z use z_tran(1).
This option will produce two additional variables based on Fisher's z: percent_replace_z and percent_sustain_z

Remarks

For a graphical illustration of the impact of a confounding variable see https://msu.edu/~kenfrank/research.htm#impact_diagram

For additional details of the calculations in a spreadsheet format and other supporting materials see https://msu.edu/~kenfrank/research.htm#causal.

For a web-based version of konfound see http://konfound-it.com.

Examples

. mkonfound var1 var2

. mkonfound var1 var2, sig(0.1) nu(.5) rep_0(1) onetail(1)

Authors

Kenneth A. Frank

Michigan State University

Ran Xu

Michigan State University

Please email ranxu@msu.edu if you observe any problems.

References

Frank, K.A. 2000. Impact of a Confounding Variable on the Inference of a Regression Coefficient. Sociological Methods and Research, 29(2), 147-194

Pan, W., and Frank, K.A. 2004. An Approximation to the Distribution of the Product of Two Dependent Correlation Coefficients. Journal of Statistical Computation and Simulation, 74, 419-443

Pan, W., and Frank, K.A., 2004. A probability index of the robustness of a causal inference. Journal of Educational and Behavioral Statistics, 28, 315-337.

*Frank, K. A. and Min, K. 2007. Indices of Robustness for Sample Representation. Sociological Methodology. Vol 37, 349-392. * co first authors.

Frank, K.A., Gary Sykes, Dorothea Anagnostopoulos, Marisa Cannata, Linda Chard, Ann Krause, Raven McCrory. 2008. Extended Influence: National Board Certified Teachers as Help Providers. Education, Evaluation, and Policy Analysis. Vol 30(1): 3-30.

Frank, K.A., Maroulis, S., Duong, M., and Kelcey, B. 2013. What would it take to Change an Inference?: Using Rubin’s Causal Model to Interpret the Robustness of Causal Inferences. Education, Evaluation and Policy Analysis. Vol 35: 437-460.