Table 2

Multivariate, multilevel models for volunteering and informal helping: Health and Retirement Study, 1998–2018

UnadjustedAdjusted
VolunteeringInformal HelpingVolunteeringInformal Helping
β95% CIβ95% CIβ95% CIβ95% CI
Fixed Effects         
 Age linear −0.120 [–0.139,–0.107] −0.112 [–0.121,0.000] −0.101 [–0.115,–0.081] −0.104 [–0.113,–0.092] 
 Age quadratica 0.091 [−0.020, 0.182] −0.747 [–0.835,–0.586] −0.205 [–0.321,–0.093] −0.401 [–0.467,–0.328] 
 Age cubicb −0.096 [–0.124,–0.068] −0.049 [–0.079,–0.023] −0.148 [–0.177,–0.116] −0.092 [–0.128,–0.053] 
 10-year cohort         
  1919–1928 0.637 [0.467,0.765] 0.373 [0.308,0.437] 0.387 [0.238,0.510] 0.269 [–0.128,–0.053] 
  1929–1938 0.995 [0.796,1.124] 0.812 [0.756,0.876] 0.628 [0.486,0.741] 0.633 [0.586,0.713] 
  1939–1948 1.086 [0.898,1.210] 1.061 [1.010,1.107] 0.609 [0.465,0.718] 0.815 [0.764,0.888] 
  1949–1958 1.225 [1.043,1.350] 1.216 [1.162,1.274] 0.615 [0.503,0.713] 0.912 [0.861,0.978] 
 Age linear × cohort         
  × 1919–1928 0.047 [0.034,0.065] 0.005 [−0.003, 0.014] 0.026 [0.006,0.042] 0.003 [−0.008, 0.012] 
  × 1929–1938 0.106 [0.093,0.125] 0.046 [0.038,0.054] 0.091 [0.069,0.105] 0.042 [0.031,0.050] 
  × 1939–1948 0.123 [0.110,0.143] 0.072 [0.063,0.081] 0.109 [0.086,0.123] 0.068 [0.056,0.077] 
  × 1949–1958 0.100 [0.086,0.119] 0.085 [0.076,0.095] 0.077 [0.056,0.092] 0.078 [0.065,0.087] 
 Age quadratic × cohorta         
  × 1919–1928 −0.531 [–0.661,–0.391] 0.469 [0.302,0.583] −0.422 [–0.574,–0.256] 0.131 [0.016,0.243] 
  × 1929–1938 −0.400 [–0.490,–0.311] 0.585 [0.427,0.680] −0.262 [–0.382,–0.134] 0.264 [0.181,0.335] 
  × 1939–1948 −0.231 [–0.316,–0.131] 0.707 [0.544,0.802] −0.067 [−0.190, 0.054] 0.387 [0.305,0.466] 
  × 1949–1958 −0.011 [−0.141, 0.116] 0.772 [0.590,0.900] 0.208 [0.045,0.361] 0.444 [0.339,0.560] 
 Covariates         
  Female 0.162 [0.126,0.209] −0.326 [–0.354,–0.299] 0.085 [−0.399, 0.125] −0.345 [–0.377,–0.318] 
  Race/ethnicity         
   Non-Hispanic Black −0.151 [–0.197,–0.105] −0.404 [–0.434,–0.372] 0.019 [−0.058, 0.096] −0.232 [–0.267,–0.196] 
   Non-Hispanic other −0.360 [–0.488,–0.194] −0.399 [–0.479,–0.308] −0.284 [–0.389,–0.174] −0.315 [–0.390,–0.227] 
   Hispanic −1.028 [–1.088,–0.961] −1.083 [–1.127,–1.041] −0.310 [–0.399,–0.229] −0.683 [–0.731,–0.633] 
  Coupled     0.073 [0.046,0.102] −0.032 [–0.053,–0.010] 
  Education in years     0.204 [0.193,0.212] 0.086 [0.081,0.091] 
  Household wealthc     0.042 [0.037,0.048] 0.028 [0.024,0.033] 
  Working for pay     0.045 [0.015,0.073] 0.041 [0.021,0.065] 
  Religious     1.093 [1.057,1.135] 0.228 [0.201,0.258] 
  ADL limitationsd     −0.251 [–0.267,–0.236] −0.255 [–0.266,–0.243] 
  Attrition −0.105 [–0.199,–0.025] 0.009 [−0.049, 0.067] −0.199 [–0.304,–0.100] −0.054 [−0.113, 0.005] 
 Intercept −1.812 [–1.928,–1.639] −0.438 [–0.496,–0.385] −2.468 [–2.551,–2.319] −0.516 [–0.568,–0.444] 
Selected Random Effects        
 Intercept 2.787 [2.686,2.889] 0.968 [0.936,0.998] 2.600 [2.513,2.702] 0.838 [0.792,0.871] 
  Cov(volunteering, helping) 0.973 [0.935,1.009]   0.750 [0.718,0.786]   
 Age 0.001 [0.000,0.002] 0.001 [0.000,0.001] 0.012 [0.011,0.013] 0.003 [0.001,0.004] 
  Cov(volunteering, helping) −0.0002 [−0.0004, 0.00001]   0.003 [0.002,0.003]   
 Intercept-slope covariance 0.017 [0.013,0.024] 0.014 [0.011,0.018] 0.030 [0.023,0.039] 0.013 [0.011,0.015] 
UnadjustedAdjusted
VolunteeringInformal HelpingVolunteeringInformal Helping
β95% CIβ95% CIβ95% CIβ95% CI
Fixed Effects         
 Age linear −0.120 [–0.139,–0.107] −0.112 [–0.121,0.000] −0.101 [–0.115,–0.081] −0.104 [–0.113,–0.092] 
 Age quadratica 0.091 [−0.020, 0.182] −0.747 [–0.835,–0.586] −0.205 [–0.321,–0.093] −0.401 [–0.467,–0.328] 
 Age cubicb −0.096 [–0.124,–0.068] −0.049 [–0.079,–0.023] −0.148 [–0.177,–0.116] −0.092 [–0.128,–0.053] 
 10-year cohort         
  1919–1928 0.637 [0.467,0.765] 0.373 [0.308,0.437] 0.387 [0.238,0.510] 0.269 [–0.128,–0.053] 
  1929–1938 0.995 [0.796,1.124] 0.812 [0.756,0.876] 0.628 [0.486,0.741] 0.633 [0.586,0.713] 
  1939–1948 1.086 [0.898,1.210] 1.061 [1.010,1.107] 0.609 [0.465,0.718] 0.815 [0.764,0.888] 
  1949–1958 1.225 [1.043,1.350] 1.216 [1.162,1.274] 0.615 [0.503,0.713] 0.912 [0.861,0.978] 
 Age linear × cohort         
  × 1919–1928 0.047 [0.034,0.065] 0.005 [−0.003, 0.014] 0.026 [0.006,0.042] 0.003 [−0.008, 0.012] 
  × 1929–1938 0.106 [0.093,0.125] 0.046 [0.038,0.054] 0.091 [0.069,0.105] 0.042 [0.031,0.050] 
  × 1939–1948 0.123 [0.110,0.143] 0.072 [0.063,0.081] 0.109 [0.086,0.123] 0.068 [0.056,0.077] 
  × 1949–1958 0.100 [0.086,0.119] 0.085 [0.076,0.095] 0.077 [0.056,0.092] 0.078 [0.065,0.087] 
 Age quadratic × cohorta         
  × 1919–1928 −0.531 [–0.661,–0.391] 0.469 [0.302,0.583] −0.422 [–0.574,–0.256] 0.131 [0.016,0.243] 
  × 1929–1938 −0.400 [–0.490,–0.311] 0.585 [0.427,0.680] −0.262 [–0.382,–0.134] 0.264 [0.181,0.335] 
  × 1939–1948 −0.231 [–0.316,–0.131] 0.707 [0.544,0.802] −0.067 [−0.190, 0.054] 0.387 [0.305,0.466] 
  × 1949–1958 −0.011 [−0.141, 0.116] 0.772 [0.590,0.900] 0.208 [0.045,0.361] 0.444 [0.339,0.560] 
 Covariates         
  Female 0.162 [0.126,0.209] −0.326 [–0.354,–0.299] 0.085 [−0.399, 0.125] −0.345 [–0.377,–0.318] 
  Race/ethnicity         
   Non-Hispanic Black −0.151 [–0.197,–0.105] −0.404 [–0.434,–0.372] 0.019 [−0.058, 0.096] −0.232 [–0.267,–0.196] 
   Non-Hispanic other −0.360 [–0.488,–0.194] −0.399 [–0.479,–0.308] −0.284 [–0.389,–0.174] −0.315 [–0.390,–0.227] 
   Hispanic −1.028 [–1.088,–0.961] −1.083 [–1.127,–1.041] −0.310 [–0.399,–0.229] −0.683 [–0.731,–0.633] 
  Coupled     0.073 [0.046,0.102] −0.032 [–0.053,–0.010] 
  Education in years     0.204 [0.193,0.212] 0.086 [0.081,0.091] 
  Household wealthc     0.042 [0.037,0.048] 0.028 [0.024,0.033] 
  Working for pay     0.045 [0.015,0.073] 0.041 [0.021,0.065] 
  Religious     1.093 [1.057,1.135] 0.228 [0.201,0.258] 
  ADL limitationsd     −0.251 [–0.267,–0.236] −0.255 [–0.266,–0.243] 
  Attrition −0.105 [–0.199,–0.025] 0.009 [−0.049, 0.067] −0.199 [–0.304,–0.100] −0.054 [−0.113, 0.005] 
 Intercept −1.812 [–1.928,–1.639] −0.438 [–0.496,–0.385] −2.468 [–2.551,–2.319] −0.516 [–0.568,–0.444] 
Selected Random Effects        
 Intercept 2.787 [2.686,2.889] 0.968 [0.936,0.998] 2.600 [2.513,2.702] 0.838 [0.792,0.871] 
  Cov(volunteering, helping) 0.973 [0.935,1.009]   0.750 [0.718,0.786]   
 Age 0.001 [0.000,0.002] 0.001 [0.000,0.001] 0.012 [0.011,0.013] 0.003 [0.001,0.004] 
  Cov(volunteering, helping) −0.0002 [−0.0004, 0.00001]   0.003 [0.002,0.003]   
 Intercept-slope covariance 0.017 [0.013,0.024] 0.014 [0.011,0.018] 0.030 [0.023,0.039] 0.013 [0.011,0.015] 

Notes: Sample N = 29,816 (180,465 person-wave observations). The table displays posterior means for the coefficients and 95% Bayesian credible intervals (CIs). CIs are based on the 2.5th and 97.5th quantiles of the posterior distribution; Bayesian CIs that do not contain zero are shown in bold. ADL = activities of daily living.

a

Estimates are multiplied by 100 to reduce leading zeros.

b

Estimates are multiplied by 1,000 to reduce leading zeros.

c

Transformed by the inverse hyperbole sine.

d

Count of five ADL limitations.

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