ci {rineq}

Calculates different type of concentration indexes

Description

This function calculates the relative concentration index (Kakwani et al.), the generalized concentration index (Clarke et al., 2002), the Wagstaff index for bounded variables (Owen et al. 2016), and the concentration index with Erreygers' correction (Erreygers et al., 2009). It returns an object of class hci for which confidence intervals, summaries and plots are defined.

Usage

ci(
  ineqvar,
  outcome,
  weights = NULL,
  type = c("CI", "CIg", "CIc", "CIw"),
  method = c("linreg_delta", "linreg_convenience", "cov_convenience", "direct"),
  df_correction = TRUE,
  robust_se = FALSE,
  rse_type = "HC3"
)

Arguments

ineqvar

Used for ranking, usually relates to the socioeconomic position, for example income.

outcome

The variable in which the inequality should be measures, for example health.

weights

Optional, used to weigh the observations. Defaults to equal weights for all observations.

type

Character, the type of concentration index to be calculated: relative concentration index (CI, default), generalized concentration index (CIg), concentration index with Erreygers Correction CIc, or Wagstaff concentration index suitable for bounded and binary outcomes CIw

method

Character, defines the calculation method. One of:

• linreg_delta: Based on linear regression without transforming the left hand side variable. Computes correct standard errors that take into account the sampling variability of the estimate of the mean (O’Donnell et al. 2008, Owen et al. 2016)

• linreg_convenience): Based on simpler regression with transformed left hand side variable. Standard errors do not take into account thee sampling variability of the estimate of the mean(O’Donnell et al. 2008, Owen et al. 2016)

• cov_convenience: Based on covariance. Equivalent to linreg_convenience (O’Donnell et al. 2008, Owen et al. 2016)

• direct: Using direct formula, standard errors do no take weighting appropriately into account (O’Donnell et al. 2008, Kakwani et al. 1997)

df_correction

If TRUE (default), calculates the concentration index based on the population variance (derived from the sample variance).

robust_se

Uses robust standard errors if TRUE. Only available for the ⁠linreg_*⁠ type methods. Requires the sandwich package.

rse_type

Character, type argument for the vcovHC(). HC3' is suggested as default, set to HC1 for Stata compatibility. See ?sandwich::vcovHC() for options.

Value

An S3 object of class hci. Contains:

• concentration_index The concentration index

• type The type

• method The method used for calculation

• variance The variance,used for calculation of confidence intervals

• fractional_rank Computed fractional rank NA

• outcome Outcome after removing NA

• call Call signature

• n Number of observations after removing NA

• robust_se Were robust standard errors calculated?

• rse_type Type of robust standard errors.

• df_correction Do the degrees of freedom correspond to a sample?

References

Clarke, P. M., Gerdtham, U. G., Johannesson, M., Bingefors, K., & Smith, L. (2002). On the measurement of relative and absolute income-related health inequality. Social Science & Medicine, 55(11), 1923-1928

Erreygers, G. (2009). Correcting the concentration index. Journal of health economics, 28(2), 504-515

Kakwani, N., Wagstaff, A., & Van Doorslaer, E. (1997). Socioeconomic inequalities in health: measurement, computation, and statistical inference. Journal of econometrics, 77(1), 87-103.

O'Donnel, O., O'Neill S., Van Ourti T., & Walsh B. (2016). Conindex: Estimation of Concentration Indices. The Stata Journal 16(1): 112-138.

O’Donnell, O., Van Doorslaer, E. , Wagstaff, A., Lindelow, M., 2008. Analyzing Health Equity Using Household Survey Data: A Guide to Techniques and Their Implementation, World Bank Publications. The World Bank.

Examples

# Direct
data(housing)
ci.bmi <- ci(ineqvar = housing$income, outcome = housing$bmi, method = "direct")
summary(ci.bmi)

# retrieve value
ci.bmi$concentration_index

# obtain confidence intervals
confint(ci.bmi, level = 0.95) 

plot(ci.bmi)

# Wagstaff type with binary outcome and robust standard errors 
# that should correspond to Stata (depends on 'sandwich'):


ci.bmi.b <- ci(housing$income, housing$high.bmi, type = "CIw", robust_se = TRUE, 
   rse_type = "HC1")