A la garantía de la no repetición:

Below I describe practical considerations in implementing the MI procedure:

1) Imputed variables: MI should be tailored to the analytical model of interest. In addition, “the number of variables in the imputation model cannot exceed the number of cases” (Enders, 2010, p. 269).17 As Allison (2010, p. 646) writes: “For MI to perform optimally, the model used to impute the data must be ‘‘congenial’’ … with the model intended for analysis. The models need not be identical, but the imputation model must generate imputations that reproduce the major features of the data that are the focus of the analysis. That is the main reason I recommend that the imputation model include all variables in the model of interest.”

In my model, I chose 21 variables for imputation: 11 that were included in the regression analysis, 4 were the paradigms and strategies excluded following the t-test, and 6 additional variables were expected to be important predictors – budget and different binary characteristics depicting the type of organization (Table 4.1). I generated 20 imputed datasets (m=20) in addition to the original. Following this imputation process, there were 2100 records in the dataset,

simulating a sample of 100 observations (100 + [20 x 100]).

2) Imputation of transformed variables: a question arises as to how to deal with transformed variables; for example: should skewed variables be logged before the MI phase or not? Empirical studies suggest that normality violations of variables may not pose a serious threat to the multiple imputation parameter estimates (Enders, 2010). Von Hippel (2009) recommended the ‘transform, then impute’ method—i.e., “calculate the interactions or squares in the incomplete data and then

17 _{This is mostly because the imputed data contain linear dependencies that cause mathematical difficulties for}

impute these transformations like any other variable.” The transform-then-impute method yields good regression estimates, even though the imputed values are often inconsistent with one another. Therefore, in cases where continuous variables were highly skewed, they were logarithmized before the imputation phase; see also (Allison, 2010, p. 645).

Table 4.1: Summary of variables used in the imputation model and % of missingness (n=100)

Variable name Label % Missing

(1) p8q2_3_4 % foundation funding 0.0 (2) ln_foundation Log % foundation funding 0.0 (3) ln_age Age of organization 0.0 (4) Geo_local_national Geographic orientation 6.0 (5) ln_employ Size (# of employees) 5.0

(6) ln_p5q1 Active members 2.0

(7) p14q2_R Volunteer dependence 10.0

(8) R_q1p7 Legal status 0.0

(9) R_Board_size Board size 8.0

(10) p10q6_6_7 Target: Government 13.0 (11) p10q6_2_3 Target: Business 13.0 (12) p10q6_1_9 Target: Individuals 13.0 (13) parad_sustain Paradigm: Sustainability 9.0 (14) parad_pub_health Paradigm: Public Health 9.0 (15) parad_conserv Paradigm: Nature Conservation 9.0

(16) p7q17 Using freelancers 4.0

(17) p4q1_1 Type: National advocacy 0.0 (18) p4q1_11 Type: Professional 0.0 (19) R_p4q1_2_3_13 Type: Community-based 0.0 (20) R_p4q1_5_12 Type: Activist / Volunteer 0.0 (21) p6q1_b_calc Budget categorical 0.0

3) Percent of missingness possible to handle: While biased estimations will certainly increase as the rates of missing data increase, accurate estimates were found as long as missingness was up to approximately 25% (Enders, 2010). Table 4.1 demonstrates that no variable in the dataset used has missingness higher than 13%. Table 4.2 displays the number of missing values for each case record. There were 69 cases with no missing values, 15 with only

one missing value, and in 2 cases, there were 7 missing values out of the 11 independent variables in the regression. All missing cases were imputed in the MI procedure.

Table 4.2: Within-case missing values (n=100)

How many variables are missing? % of cases

0 69.0 1 15.0 2 5.0 3 5.0 4 3.0 5 1.0 7 2.0 Total 100.0

4) Scale imputation: imputation should ideally be performed at the level of scale items. However, since answers were forced in this study, scales were either fully complete (no single- items missingness), or the entire scale was completely missing. Under such conditions, item-level imputation is not necessary; instead, the scale level imputation method is the best available method (Enders, 2010, p. 270). Each scale was analyzed first for underlying latent components using Principal Component Analysis (PCA) and sub-scale components (or factors) were created (see Tables 4.3 & 4.4 below). Consequently, the imputed data are at the level of components.18 The advantage of imputation at the component level is that it dramatically reduces the number of variables for imputation. The limits are that scale-level imputation reduces statistical power and increases the standard error by up to 10% (Enders, 2010).

5) Rounding and out of range values: The ice imputation method does not implement range restrictions on imputed values (apart from models for interval-censored data). As a result,

imputed values are not necessarily integers, as the survey results are, and might also fall outside the range of values for the variable (for example, negative values for percent of foundation donations). Allison (2010, p. 645), however, suggested that, “imposing upper and lower bounds on imputed values can lead to bias because it inappropriately reduces variances,” and that, “linear imputation models usually do a satisfactory job with non-normal variables, [so] the best

18 _{The mim command does not accept computer produced factor variables, so I computed the components manually (see:}

practice is to leave the imputed values as they are, even if those values are unlike the real values in some respects.” I follow Allison’s (2010) recommendation in my analysis, despite practice in previous studies of philanthropy to substitute out of range values with positive values (e.g., (Wiepking, 2007).