In this study, two sets of quantitative analyses are performed. In the first set, the effect of team membership on lending behavior is estimated. Subsequently, in the second set, a similar estimation is made of the effect of the effect of lending behavior of team captains on that of team members. Each set consists of two analysis; one in which lending frequency is estimated and one in which lending amount is estimated. In all analysis the effect of time on lending behavior is controlled for. With the latter check, the possibility that lending behavior changes naturally over time is taken into account. This check is performed with and without an assumption of linearity.
Two datasets are constructed based on the collected data. The data in these sets have been arranged to be in “vertical format”, where there are several cases (or rows) corresponding to observations on an individual unit of analysis (lender) collected over time (West, 2009; Peugh & Enders, 2005). The data are then analysed using LMMs (linear mixed models). Because these data are taken from the day-to-day practice of Kiva.org, ecological validity is assumed to be higher than that of experimental studies. The dataset contains all lending actions by non-anonymous lenders. Diversity among these lenders is presumed to be high, because Kiva.org hosts an internation platform. On this basis, external validity is assumed.
The datasets have three important features that have implications for the analysis. Firstly, two observations of lending behavior for the same unit of analysis (lender) cannot be assumed to be independent. The can be expected to have covariance, because they describe the behavior of the same individual. Therefore, in the LMMs, the estimation includes assumptions in the form of a covariance structure. By doing this, systematic controlling is performed for the possiblity that lenders that join teams lend more in the first place. Two different covariance structures are tested for the first dataset. These are the autoregressive and heterogeneous autoregressive covariance structures. Both structures take into account covariance between observations on the same unit of analysis. Observations that are more close to each other in time, are assumed to correlate more than observations that are spaced further apart (West, 2009). In contrary to the ‘regular’ autoregressive covariance structure, the heterogeneous structure accounts for the possibility that the correlations between observations differ per set of observations. Technical limitations in the statistical processor (SPSS) limit the tests of covariance structures to ‘regular’ autoregressive models for the second dataset.
Secondly, the amount of observations and the times at which observations are performed differ per unit of analysis; the dataset is unbalanced. The statistical model used should account for these features. OLS, like those employed by Liu et al. (2012), do not account for these features. Linear Mixed Model analysis does (West, 2009; Peugh & Enders, 2005).
Thirdly, the dependent variables are distributed lognormally. To normalise these variables a log transformation is performed on them, following the method of Liu et al. (2012). This influences the way the results should be interpreted. The estimated bèta values should be interpreted as percentual changes in the dependent variable due to a change of 1 in the unit of measure for the independent variable (Kephart, 2013; Yang, 2012).
For higher content validity, the estimated models are tested on two levels. Firstly, for the analysis of the general effect of team membership on lending behavior, tests are performed for the best fit based on covariance structures. Best fit is characterized by a lower -2 log likelihood value for the estimated model in comparison with other models. These are likelihood ratio tests (Peugh & Enders, 2005). The content validity for the second set of analysis is limited, because the likelihood ratio tests cannot be performed due to technical limitations of the statistical processor. Secondly, further likelihood ratio tests are perform to test the relevance of the parameters in the models. Stepwise, the most complex model is reduced by excluding independent variables. By comparing the -2 log likelihood values for each model, hypothesis about the effect of independent variables in the models can be tested (Peugh & Enders, 2005).
Analysis of the effect of team memberships on lending behavior
The dataset designed for testing the effect of team membership on lending behavior features a new observation (row) for each time a lender joins a (or an extra) team. The observation contains all lending activity until the time at which the lender joins another team, or data collection ends. Observed are the amount of team memberships, the lending frequency and lending amount for the recorded period of time. In the first set of analysis, variability in lending behavior is measured within persons (within sets of observations for a lender) en between persons (between sets of observations of lenders). Both are analysed taking account of the effect of time. The amount of team memberships, that differs per lender per observation (increases with the amount of observations), is the independent variable. Lending frequency and lending amount are depedent variables. Two models are estimated to measure the effect of team membership on lending frequency and lending amount.
Analysis of the modelling effect
To simplify the method of analysis for this set of analysis, a cumulative modelling effect is ruled out. This is done on three levels. Firstly, by preselecting the lending actions of team captains to make sure that, in a period of 48 hours around a captain’s lending action, no other lending actions were performed by the team captain. This prevents a cumulative effect originating from one team captain. Secondly, by selecting only teams with exactly one team captain, a cumulative effect within teams originating from multiple team captains is ruled out. Thirdly, team members are selected so that only team members that are members of exactly one team are included in the dataset. By doing this the possibility that multiple teams influence the member’s lending behavior is ruled out. These selections reduce the construct validity of the analysis and limit the possibility of generalizing the results to situations where no cumulative modelling effect is present. Taking into account a cumulative modelling effect would greatly increase the construct validity.
After these preselections, for each team captain a random lending action is selected using the MySQL RAND() function. For each member of the captain’s team (and only that team) in the period of 48 hours around the captain’s lending action, two observations (rows) are recorded. On observation regards the 24 hours before the captain’s lending action, the other the 24 after the captain’s lending action. For each observation the lending frequency and lending amount in that period are recorded. Using a dummy variable, the first 24 hours are marked as unconditioned, the latter conditioned. All lending actions by team members, in these periods, are included in the sample.
The analysis of the modelling effect is performed by estimating models for the variance in lending behavior of team members within persons (within sets of observations for a lender), over time and combined with state of conditioning. Lending frequency and lending amount are dependent variables. Two models are estimated to measure the effect of conditioning on lending frequency and lending amount (modelling effects).