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我希望评估成为多数人的一部分如何有助于成为动物群体的领导者。

假设我有 10 个案例来评估领导者是来自多数还是少数。

Leader <- c(1,1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0,0,1,0)
Case <- as.factor(c(1,2,3,4,5,6,7,8,9,10,1,2,3,4,5,6,7,8,9,10))
Majority <- as.factor(c("Maj","Maj","Maj","Maj","Maj","Maj","Maj","Maj","Maj","Maj",
        "Min","Min","Min","Min","Min","Min","Min","Min","Min","Min"))
leadMaj <- data.frame(Leader,Case,Majority)

binomial.glmer <- glmer(Leader ~ Majority + (1|Case),
                    family = binomial, data = leadMaj)
summary(binomial.glmer)

结果表明，来自少数群体会大大降低领导团队的可能性

Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) [glmerMod]
Family: binomial  ( logit )
Formula: Leader ~ Majority + (1 | Case)
Data: leadMaj

 AIC      BIC   logLik deviance df.resid 
  26       29      -10       20       17 

Scaled residuals: 
Min     1Q Median     3Q    Max 
-2.0   -0.5    0.0    0.5    2.0 

Random effects:
Groups Name        Variance Std.Dev.
Case   (Intercept) 0        0       
Number of obs: 20, groups:  Case, 10

Fixed effects:
        Estimate Std. Error z value Pr(>|z|)  
(Intercept)   1.3863     0.7906   1.754   0.0795 .
MajorityMin  -2.7726     1.1180  -2.480   0.0131 *
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Correlation of Fixed Effects:
            (Intr)
MajorityMin -0.707

然而，这些群体由 8 人占多数，2 人占少数。我们可以看到，在 80% 的情况下，多数人领先，这是预期的。

所以问题是：如何包含 p=0.8 而不是 p=0.5 的二项分布？

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