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I am currently researching which non-profit organisations would voluntarily appoint an auditor. One of my hypotheses is that NPO's that depend on grants and donations are more likely to voluntarily appoint an auditor. However, NPO's are not obliged to disclose the amount of donations and grants they receive. So of the population of 4,510 NPO's, only 1,610 disclose how much grants and donations they receive.

My idea to resolve this problem is to is to include a dichotomous variable $Z$ for whether the NPO discloses grant funding or not; a continuous variable $X$ for the amount of funding, to which you would assign 0 to the nondisclosers; and a term $Z \times X$ for their interaction.

Blank answers would be replaced with value 0. My only question is if this is considered a valid option and doesnt create any problems.

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  • $\begingroup$ Depending on grants/donations is different from receiving grants/donations. You need to collect more information to classify NPOs as dependent. $\endgroup$ – AdamO Apr 24 '18 at 12:13
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I suspect that this would distort the model's parameter estimates. It would likely be preferable to not include an indicator variable of missingness but to set amounts not disclosed to missing and use multiple imputation. This will also result in appropriate standard errors. A guiding principle is to try to make the model parameters have the same interpretation whether you have missing data or not.

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    $\begingroup$ Multiple imputation is okay if the data are missing at random. I suspect the disclosure of grant/donation revenue is highly related to the amount of grants/donations an NPO receives. High revenue places could be more likely to disclose. $\endgroup$ – AdamO Apr 24 '18 at 12:15
  • $\begingroup$ Sowhat are my options then? and why would the inclusion of the indicator variable cause a problem? $\endgroup$ – Latriuz Apr 24 '18 at 12:46
  • $\begingroup$ There is a hope that there will be missing at random conditional on the outcome variable, all other predictors, and perhaps auxiliary variables not wanted for inclusion in the outcome model. Unless you have a correct selection model for self-disclosure we don't have much to do other than missing at random-based multiple imputation (I prefer predictive mean matching as the imputation method). $\endgroup$ – Frank Harrell Apr 25 '18 at 12:50

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