Results

Firstly, results of the analysis of the general effect of team memberships on lending behavior are discussed. The likelihood ratio tests for the covariance structures are discussed. Subsequently the likelihood ratio tests for the model parameters are addressed, then the effects of the parameters are discussed. Secondly the results of the second set of analysis are discussed, concerning the modelling effect of team captains on team member’s lending behavior. De results of the likelihood ratio tests for the model parameters are discussed and the effects of the parameters are described.

The effect of team membership on lending behavior

Analysis of the effect of team membership on lending frequency
Analysis 1.1 covers the analysis of the effect of team membership on lending frequency. The results are displayed in Table 1. Two covariance structures have been tried for this analysis. Models with a heterogeneous autoregressive covariance structure (ARh1) have a consistent better fit than the models with assumed homogeneous relationships between subsequent observations. (AR1). This can be seen by the consistently lower -2 log likelihood values noted for the models with an ARH1 covariance  structure compared to the -2 log likehood values for the models with an AR1 covariance structure.

Table 1: Results analysis 1.1, Effect of team membership on lending frequency

Model 1

Model 2

Model 3

Model 4

Model 5

Model 6

Intercept

1.465*** (.018)

1.383*** (.020)

1.387***
(.035)

1.288***
(.042)

1.398***
(.055)

1.402***
(.082)

Team membership

-.002

(.001)

-.002

(.001)

.011***
(.003)

.012***
(.003)

-.012*
(.005)

Time

.000
(.000)

.001*
(.000)

-.004*
(.002)

-0.004

(.002)

Time * Team membership

-.000***
(.000)

-.000***
(.000)

-.000
(.000)

Time * Time

.49**
(.16)

.51*
(.20)

Time * Time * Team membership

.000
(.01)

N rows

3162

3162

3162

3162

3162

3162

N subjects

1556

1556

1556

1556

1556

-2 Restricted Log Likelihood (AR1)

8868.943

8725.008

8721.628

8732.070

8729.239

8748.345

-2 Restricted Log Likelihood (ARH1)

8868.943

[1066.451***]

7802.492
[-13.410***]

7815.902
[-1.384]

7817.286
[-11.052***]

7828.338
[-24.998***]

7853.336

Note: Standard errors in parenthesis. Deviances of subsequent models in square brackets.

Results multiplied by 10.000

* p < .05, ** p < .01, *** p < .001

Subsequent models with decreasing complexity (counting down from model 6) show, based on the difference in -2 log likelihood values, that only removal of the team membership variable results in significant worse fit of the model, as shown by the significant positive deviance of the -2 log likehood value for Model 1 of 1066.451 (p < 0.001). Adding variables that control for an effect of time on lending frequency leads to significant worse fits for alternative models. Based on these results it can be assumed that the parameters added in Model 3 – 6 can be safely removed without lowering the model’s fit. The effects of these parameters are not evaluated for this reason.

Model 2 provides the best fit for the effect of team membership on lending frequency. This appears to be mainly due to the application of the heterogeneous covariance structure; the null hypothesis that, the effect of team membership on lending frequency is equal to 0, must be accepted (p = .115). The effect of team membership on lending frequency is not significant. The alternative hypothesis, stating that team membership effects lending frequency, is rejected.

Analysis of the effect of team membership on lending amount
Analysis 1.2 covers the analysis of the effect of team membership on lending amount. The results are displayed in Table 2. Again two covariance structures have been tried for this analysis. Models with a heterogeneous autoregressive covariance structure (ARh1) have a consistent better fit than the models with assumed homogeneous relationships between subsequent observations. (AR1). This can be seen by the consistently lower -2 log likelihood values noted for the models with an ARH1 covariance  structure compared to the -2 log likehood values for the models with an AR1 covariance structure.

Table 2: Results analysis 1.2, Effect of team membership on loan amount

 
 

Model 1

Model 2

Model 3

Model 4

Model 5

Model 6

Intercept

1.891***

(.020)

1.823***
(.029)

2.071***
(.053)

1.937***
(.060)

2.072***
(.082)

2.033***
(.090)

Team membership  

.017***
(.003)

.017***
(.003)

.049***
(.007)

.049**
(.007)

.058***
(.011)

Time

-.004***
(.001)

-.002*
(.001)

-.009**
(.003)

-.007*
(.003)

Time * Team membership

-.000***

(.000)

-.001***
(.000)

-.001*
(.000)

Time * Time

.58*

(.24)

.43
(.28)

Time * Time * Team membership

.04
(.03)

N rows

3162

3162

3162

3162

3162

3162

N subjects

1556

1556

1556

1556

1556

-2 Restricted Log Likelihood (AR1)

9832.052

9413.198

9399.304

9399.272

9413.549

9436.633

-2 Restricted Log Likelihood (ARH1) 9832.052
[438.939]
9393.113
[18.004***]
9375.109
[5.608*]
9369.501
[-13.599***]
9383.100
[-22.375***]

9405.475

Note: Standard errors in parenthesis. Deviances of subsequent models in square brackets.

† Results multiplied by 10.000

* p < .05, ** p < .01, *** p < .001

Analysis shows, by comparing the -2 log likelihood values for nested models, that the model fit significantly worsens after removing the interaction variables and the variables included in this interaction effect. This can be seen when evaluating the significant positive deviance of the -2 log likehood value for Model 3 compared to Model 4, the latter of which has the interaction effect added, of 5.608 (p < 0.05), the significant positive deviance of Model 2 compared to Model 3, the latter of which has the variable time added, of 18.004 (p < 0.001) and the significant positive deviance of Model 1 compared to Model 2, the latter of which has the team membership variable and covariance structure added, by 438.939 (p < 0.001).

Adding the variables that control for an exponential relationship with time and the interaction of time with the increase of team memberships, lead to significant worse fits for the alternative models. Based on these results it is assumed that the parameters added in Model 5 and 6 can be discarded without lowering the model’s fit. The effects of these parameters are not evaluated for this reason.

Model 4 provides the best fit for variance in lending amounts. The effect of team membership in this model is significant, estimated at 0.049 (p = .000). This can be interpreted as an increase of 4.9% in lending amount with every extra team membership that a lender enters into. This effects goes along with a significant effect of time and the interaction effect of time with team membership. Over time lending amount decreased, it decreases with 0.19% (p = 0.022) per day. The interaction effect describes how team memberships effect lending amount over time. This effect is estimated to result in a decrease of lending amounts by 0.05% (p = .000) per day.

The modelling effect

Analysis of the effect of lending by team captains on lending frequency of team members
Analysis 2.1 covers the analysis of the modelling effect on lending frequency. No alternative covariance structures are considered for this analysis. Table 3 displays the results of this analysis. They show significant worse fits when variables are added to form more complex models. This shows that none of the indepedent variables explain the variance in team member’s lending frequency. The null hypothesis, that conditioning by a team captain has no effect on lending frequency must be accepted based on the likelihood ratio tests. They show that adding parameters needed to analyse the modelling effect, lead to significant positive deviance of the model’s -2 log likelihood value. This holds true for Model 1 compared to Model 2, for Model 2 compared to Model 3 and Model 3 compared to Model 4. The respective deviances are 7.604 (p < .05), 11.967 (p < .01) and 19.03 (p < .01).

Table 3: Results analysis 2.1, Effect of team captains on lending frequency

 
 

Model 1

Model 2

Model 3

Model 4

Model 5

Model 6

Intercept

1.113***
(.001)

1.116***

(.001)

1.116***
(.001)

1.116***
(.001)

1.113***
(.002)

1.114***
(.002)

Time  

-.000***

(.000)

-.000***

(.000)

-.000**
(.000)

.000*
(.000)

.000
(.000)

Conditioning    

-.000
(.001)

-.000
(.002)

-.001
(.002)

-.003
(.003)

Time * Conditioning  

.000
(.000)

.000
(.000)

.000
(.000)

Time * Time  

-.02***
(.01)

-.01
(.01)

Time * Time * Conditioning  

.-01
(.01)

N rows 35184 35184 35184 35184 35184

35184

N subjects   17592 17592 17592 17592

17592

-2 Restricted Log Likelihood (AR1) -66380.336

[-7.604**]

-66372.732
[-11.967***]
-66360.764
[-19.03***]
-66341.734
[-16.585***]
-66324.876
[-24.867***]
-66300.009
Note: Standard errors in parenthesis. Deviances of subsequent models in square brackets.

† Results multiplied by 10.000

* p < .05, ** p < .01, *** p < .001

Analysis of the effect of lending by team captains on lending amount of team members
Analysis 2.1 covers the analysis of the modelling effect on lending amount. As with analysis 2.1, no alternative covariance structures are tried. Table 4 displays the results of this analysis. They show significant worse fit when the covariance structure and independent variable time are added. The null hypothesis, that further parameters lead to no better fit for the model explaining variance in lending amount, must be accepted for the other parameters. This means the alternative hypothesis, that conditioning by a team captain effects team members lending amount, must be rejected. Specifically because Model 2 compared to Model 3 shows no better fit with a deviance of -8.001 (p <.05); conditioning does not explain variance in lending amount. The effect of time in Model 2 is significantly negative, -.0003 (p = .000). This shows the effect of time noted in analysis 1.2 where the loan amount of team members slightly decreasing over time.

Table 4: Results analysis 2.2, Effect of team captains on loan amount

 
 

Model 1

Model 2

Model 3

Model 4

Model 5

Model 6

Intercept 1.177***
(.002)
1.194***
(.005)
1.196***
(.005)
1.197***
(.006)
1.173***
(.008)
1.178***

(.010)

Time   -.000***
(.000)
-.000***
(.000)
-.000***
(.000)
.001***
(.000)
.001*
(.000)
Conditioning     -.004
(.005)
-.006
(.009)
-.009
(.009)
-.018
(.014)
Time * Conditioning       .000
(.000)
.000
(.000)
.001
(.001)
Time * Time         -.12***
(.03)
-.10**
(.04)
Time * Time * Conditioning           -.05
(.05)
N rows 35184 35184 35184 35184 35184 35184
N subjects   17592 17592 17592 17592 17592
-2 Restricted Log Likelihood (AR1)

40380.063

[0.7604]

40379.299
[-8.001*]

40387.300
[-16.017***]

40403.317
[-1.725]

40405.042
[-21.701***]

40426.743

Note: Standard errors in parenthesis. Deviances of subsequent models in square brackets.

† Results multiplied by 10.000

* p < .05, ** p < .01, *** p < .001

* p < .05, ** p < .01, *** p < 0.001

Leave a Reply

Your email address will not be published. Required fields are marked *