Empirical model settings

This paper uses three HLM sub-models: the null model, the intercepts-as-outcomes model, and the intercepts-and-slopes-as-outcomes model. The dependent variable is individual income (Y), and is divided into high, medium, and low levels, where Y=1 represents agents with low incomes, Y=2 represents agents with medium incomes, and Y=3 represents agents with high incomes. The explanatory variables include GENDER, UNI (agents with an educational level of university or above), COLLEGE (agents with an educational level of college), AGE, CHILD (having a child aged under six or

Characteristic variables:

MANAGEMENT TYPE LOCATION

Independent variables:

GENDER EDUCATION AGE

MAR CHILD HOURS EXP

Dependent variable:

INDIVIDUAL INCOME

younger), HOURM (per week working 41~70 hours), HOURH (per week working 71 hours and above), EXP (work experience), and EXPS (squares of work experience).

The branch-level variables include TYPE (regular chains, franchises) and LOCATION (branch located in downtown or suburbs). Tabachnick and Fidell (2001) argue that centering can reduce the multicollinearity problems between explanatory variables.

The types of centering can be classified into group mean centering and grand mean centering. In empirical estimation, the continuous variables will be applied for centralization by using grand mean.

3.2.1 Null model

This method tests whether individual incomes at various branches are different without considering any explanatory variables. The main purpose of the model is to distinguish intra-branch (intra-group) and inter-branch (inter-group) variation in individual income.

It estimates how much variation in individual income is caused by the variation between branch stores and provides the preliminary estimated values for reference in the further analysis before considering whether HLM or general regression analysis should be applied. Utilizing terminology from Raudenbush and Bryk (2002), the model is characterized by level as follows:

Level-1 (micro-level):

indicating whether m2 (i.e., D_2ij 1 if m2, D_2ij 0 if m1). This formulation thus summarizes the two equations:

) is the overall average logit of high income agents, and u_0j is the random variation in the level-1 intercepts across branches, which represents the deviations of the j ^th branch’s mean logit from the grand mean or overall mean logit.

3.2.2 Intercepts-as-outcomes model

The intercepts-as-outcomes model mainly aims to validate the influence of explanatory variables at the micro-level and branch-level, if variables at both levels exist, on dependent variables. When the null model confirms that the inter-group variation in dependent variables is significant, the explanatory variables of agent characteristics are added at the micro-level, including GENDER, UNI, COLLEGE, AGE, MAR, CHILD, HOURM, HOURH, EXP, and EXPS. The intercept is set as a random effect. The model regards the influence of variables at the micro-level as constants. In other words, it assumes that branch-level characteristic variables are able to fully explain the variances of the dependent variables at the micro-level. Hence, TYPE_j and

LOCATION are specified to influence the intercepts of the micro-level prediction j

equations. By using the proposed model, this paper seeks to verify the impact of individual-level explanatory variables on individual income – that is, to determine

whether individual incomes are different under different management types and

For three categories, a total of two cumulative logits are formulated. The term _mij is the m th cumulative logit; p_mij is the probability of the m th income;  is the intercept or slope of the first level; and  is the intercept or slope of the second level.

The term D_2ijis a dummy variable indicating whether m2 (i.e., D_2ij 1 ifm2,

2_ij 0

D ifm1)._2j is the difference between the intercepts of two logits; u_0j is the error term, and is assumed to have a mean of zero and variance ₀₀; _0j is set as the random change; and _kj and _2j are set as the constant change. The important feature of this model is that two intercepts are different, but the slope parameters are the same in each logit (Agresti, 1989). Because intercepts have a constant value for each of the two cumulative logits, this model is also called a proportional odds model.

The terms ₀₁ and₀₂ represent the cross-level direct impact of TYPE and _j

LOCATIONj on the probability of high individual income.

3.2.3 Intercepts-and-slopes-as-outcomes model

The third model is the intercepts-and-slopes-as-outcomes model, which uses the intercepts and slopes of the individual-level as the outcome variables of the branch store level. It is a typical hierarchical linear model. The purpose of this model is to understand whether the characteristic variables of the branch stores can moderate the impact of the independent variables at the individual-level on the individual incomes.

By using the management type (TYPE) as the moderating variable, this study explored whether the effect of the explanatory variables at the individual-level on the individual income (coefficient) can be moderated by the management type.

Level-1 (micro-level):

Finally, regardless of hierarchy, the single level ordinal logit model is applied for estimation to understand the differences in estimation results and the intercepts-and-slopes-as-outcomes model. The difference between the proposed model

and the intercepts-and-slopes-as-outcomes model is that, in the proposed model, the first level intercept _0j is set as the fixed effect without the settings of random error item u_0j. The model settings are as shown in Equation (8): and agents of the same branch are regarded as members of a “working team” who have

a competitive-cooperative relationship. Hence, the variables can be divided into explanatory variables representing individuals and characteristic variables representing branches. The individual-level explanatory variables include dummy variables and continuous variables. The dummy variables for each agent include gender, educational level, marital status, whether the agent has children under six years old, management type, and branch location, while the continuous variables include age, work hours,