SEM updated
Lisa Merrill
2024-08-14
Loading libraries
library(tidyverse)## ── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
## ✔ dplyr 1.1.3 ✔ readr 2.1.4
## ✔ forcats 1.0.0 ✔ stringr 1.5.1
## ✔ ggplot2 3.4.4 ✔ tibble 3.2.1
## ✔ lubridate 1.9.3 ✔ tidyr 1.3.0
## ✔ purrr 1.0.2
## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ dplyr::filter() masks stats::filter()
## ✖ dplyr::lag() masks stats::lag()
## ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errorslibrary(lavaan)## This is lavaan 0.6-18
## lavaan is FREE software! Please report any bugs.#install.packages("semPlot")
library(semPlot)Loading data
db <- read.csv("dairymean_bone.csv")
db2 <-read.csv("dairy_TBS_BMD_cov.csv")#look at variance of inflammation biomarkers
#lapply(db,function(x)var(x,na.rm=T))#variance of each is high; log transform
db$log_crp <- log(db$CRP)
db$log_tnf <-log(db$TNFa)
db$log_IL6 <-log(db$IL6)
db$log_il1B <-log(db$IL1B)
db$log_skim <-log(db$skim)
db2 <-read.csv("dairy_TBS_BMD_cov.csv")
db2$log_crp <-log(db2$CRP)
db2$log_tnf <-log(db2$TNFa)
db2$log_IL6 <-log(db2$IL6)
db2$log_il1B <-log(db2$IL1B)
db2$log_skim <-log(db2$skim + 0.01)Eliminate bone columns 3a, 5a, 5c, 5f because of high NA content
db$bone3a_b2 <- NULL
db$bone5a_b2 <- NULL
db$bone5c_b2 <- NULL
db$bone5f_b2 <- NULL
db2$bone3a_b2 <- NULL
db2$bone5a_b2 <- NULL
db2$bone5c_b2 <- NULL
db2$bone5f_b2 <- NULLEliminate dichotomized variables
# db <- db %>% dplyr::select(!contains("dichot"))
# db2 <- db2 %>% dplyr::select(!contains("dichot"))SEM milk as predictor var, BMSi as response, and IL6, TNFa, IL1B as individual mediators
model_milk <- ' # direct effect
BMSi ~ i*milk
# mediator
IL6 ~ a*milk
TNFa ~ c*milk
IL1B ~ e*milk
CRP ~ g*milk
BMSi ~ b*IL6
BMSi ~ d*TNFa
BMSi ~ f*IL1B
BMSi~ h*CRP
# indirect effect (a*b)
ab := a*b
cd := c*d
ef := e*f
gh :=g*h
# total effect
total := i + (a*b) +(c*d) +(e*f) +(g*h)
'
fit <- sem(model_milk, data = db)
summary(fit)## lavaan 0.6-18 ended normally after 1 iteration
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 14
##
## Used Total
## Number of observations 151 163
##
## Model Test User Model:
##
## Test statistic 8.559
## Degrees of freedom 6
## P-value (Chi-square) 0.200
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Regressions:
## Estimate Std.Err z-value P(>|z|)
## BMSi ~
## milk (i) 0.958 0.852 1.125 0.261
## IL6 ~
## milk (a) -0.588 0.474 -1.241 0.215
## TNFa ~
## milk (c) 0.682 0.743 0.919 0.358
## IL1B ~
## milk (e) -1.824 2.794 -0.653 0.514
## CRP ~
## milk (g) -1.618 0.658 -2.458 0.014
## BMSi ~
## IL6 (b) -0.120 0.142 -0.847 0.397
## TNFa (d) -0.029 0.091 -0.319 0.750
## IL1B (f) -0.019 0.024 -0.768 0.442
## CRP (h) -0.079 0.102 -0.774 0.439
##
## Variances:
## Estimate Std.Err z-value P(>|z|)
## .BMSi 64.811 7.459 8.689 0.000
## .IL6 21.222 2.442 8.689 0.000
## .TNFa 52.186 6.006 8.689 0.000
## .IL1B 738.733 85.019 8.689 0.000
## .CRP 40.972 4.715 8.689 0.000
##
## Defined Parameters:
## Estimate Std.Err z-value P(>|z|)
## ab 0.071 0.101 0.699 0.484
## cd -0.020 0.066 -0.301 0.763
## ef 0.034 0.068 0.497 0.619
## gh 0.128 0.174 0.739 0.460
## total 1.171 0.833 1.405 0.160semPaths(fit)
Fluid dairy
model_fluid <- ' # direct effect
BMSi ~ i*fluid
# mediator
IL6 ~ a*fluid
TNFa ~ c*fluid
IL1B ~ e*fluid
CRP ~ g*fluid
BMSi ~ b*IL6
BMSi ~ d*TNFa
BMSi ~ f*IL1B
BMSi~ h*CRP
# indirect effect (a*b)
ab := a*b
cd := c*d
ef := e*f
gh :=g*h
# total effect
total := i + (a*b) +(c*d) +(e*f) +(g*h)
'
fit <- sem(model_fluid, data = db)
summary(fit)## lavaan 0.6-18 ended normally after 1 iteration
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 14
##
## Used Total
## Number of observations 151 163
##
## Model Test User Model:
##
## Test statistic 8.524
## Degrees of freedom 6
## P-value (Chi-square) 0.202
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Regressions:
## Estimate Std.Err z-value P(>|z|)
## BMSi ~
## fluid (i) 0.871 0.800 1.089 0.276
## IL6 ~
## fluid (a) -0.509 0.446 -1.142 0.253
## TNFa ~
## fluid (c) 0.655 0.698 0.938 0.348
## IL1B ~
## fluid (e) -1.745 2.628 -0.664 0.507
## CRP ~
## fluid (g) -1.470 0.620 -2.371 0.018
## BMSi ~
## IL6 (b) -0.122 0.142 -0.860 0.390
## TNFa (d) -0.029 0.091 -0.316 0.752
## IL1B (f) -0.019 0.024 -0.770 0.442
## CRP (h) -0.081 0.102 -0.790 0.430
##
## Variances:
## Estimate Std.Err z-value P(>|z|)
## .BMSi 64.845 7.463 8.689 0.000
## .IL6 21.255 2.446 8.689 0.000
## .TNFa 52.173 6.004 8.689 0.000
## .IL1B 738.660 85.010 8.689 0.000
## .CRP 41.082 4.728 8.689 0.000
##
## Defined Parameters:
## Estimate Std.Err z-value P(>|z|)
## ab 0.062 0.091 0.687 0.492
## cd -0.019 0.063 -0.299 0.765
## ef 0.032 0.064 0.503 0.615
## gh 0.119 0.158 0.749 0.454
## total 1.066 0.784 1.359 0.174semPaths(fit)
Total dairy
model_total <- ' # direct effect
BMSi ~ i*mod
# mediator
IL6 ~ a*mod
TNFa ~ c*mod
IL1B ~ e*mod
CRP ~ g*mod
BMSi ~ b*IL6
BMSi ~ d*TNFa
BMSi ~ f*IL1B
BMSi~ h*CRP
# indirect effect (a*b)
ab := a*b
cd := c*d
ef := e*f
gh :=g*h
# total effect
total := i + (a*b) +(c*d) +(e*f) +(g*h)
'
fit <- sem(model_total, data = db)
summary(fit, fit.measures=TRUE, standardized=TRUE)## lavaan 0.6-18 ended normally after 1 iteration
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 14
##
## Used Total
## Number of observations 151 163
##
## Model Test User Model:
##
## Test statistic 8.443
## Degrees of freedom 6
## P-value (Chi-square) 0.207
##
## Model Test Baseline Model:
##
## Test statistic 21.448
## Degrees of freedom 15
## P-value 0.123
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.621
## Tucker-Lewis Index (TLI) 0.053
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -2694.331
## Loglikelihood unrestricted model (H1) -2690.110
##
## Akaike (AIC) 5416.662
## Bayesian (BIC) 5458.904
## Sample-size adjusted Bayesian (SABIC) 5414.596
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.052
## 90 Percent confidence interval - lower 0.000
## 90 Percent confidence interval - upper 0.126
## P-value H_0: RMSEA <= 0.050 0.414
## P-value H_0: RMSEA >= 0.080 0.322
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.050
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## BMSi ~
## mod (i) 1.110 0.797 1.393 0.164 1.110 0.115
## IL6 ~
## mod (a) -0.424 0.446 -0.951 0.341 -0.424 -0.077
## TNFa ~
## mod (c) 0.407 0.698 0.583 0.560 0.407 0.047
## IL1B ~
## mod (e) -1.858 2.622 -0.708 0.479 -1.858 -0.058
## CRP ~
## mod (g) -1.603 0.616 -2.602 0.009 -1.603 -0.207
## BMSi ~
## IL6 (b) -0.122 0.142 -0.864 0.388 -0.122 -0.069
## TNFa (d) -0.027 0.090 -0.295 0.768 -0.027 -0.024
## IL1B (f) -0.018 0.024 -0.740 0.459 -0.018 -0.059
## CRP (h) -0.072 0.102 -0.703 0.482 -0.072 -0.058
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .BMSi 64.525 7.426 8.689 0.000 64.525 0.970
## .IL6 21.311 2.453 8.689 0.000 21.311 0.994
## .TNFa 52.360 6.026 8.689 0.000 52.360 0.998
## .IL1B 738.363 84.976 8.689 0.000 738.363 0.997
## .CRP 40.784 4.694 8.689 0.000 40.784 0.957
##
## Defined Parameters:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## ab 0.052 0.081 0.640 0.522 0.052 0.005
## cd -0.011 0.041 -0.263 0.792 -0.011 -0.001
## ef 0.033 0.065 0.512 0.609 0.033 0.003
## gh 0.115 0.170 0.679 0.497 0.115 0.012
## total 1.300 0.780 1.666 0.096 1.300 0.134semPaths(fit)
Adjusted milk as predictor, BMSi as response; IL6, TNFa, IL1B, CRP as individual mediators
model_milk_adj <- ' # direct effect
BMSi ~ i*milk + age_final + female_b2 + PA_SCORE_b2 + vitd_top + BMI_b2 + alcohol_freq_8yr
# mediator
IL6 ~ a*milk + diabetes_bone2
TNFa ~ c*milk + diabetes_bone2
IL1B ~ e*milk + diabetes_bone2
CRP ~ g*milk + diabetes_bone2
BMSi ~ b*IL6
BMSi ~ d*TNFa
BMSi ~ f*IL1B
BMSi ~ h*CRP
# indirect effect (a*b)
ab := a*b
cd := c*d
ef := e*f
gh := g*h
# total effect
total := i + (a*b) +(c*d) +(e*f) +(g*h)
'
fit_milk_adj <- sem(model_milk_adj, data = db)
summary(fit_milk_adj, fit.measures=TRUE, standardized=TRUE, ci=TRUE)## lavaan 0.6-18 ended normally after 1 iteration
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 24
##
## Used Total
## Number of observations 135 163
##
## Model Test User Model:
##
## Test statistic 58.634
## Degrees of freedom 31
## P-value (Chi-square) 0.002
##
## Model Test Baseline Model:
##
## Test statistic 85.289
## Degrees of freedom 50
## P-value 0.001
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.217
## Tucker-Lewis Index (TLI) -0.263
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -2418.221
## Loglikelihood unrestricted model (H1) -2388.904
##
## Akaike (AIC) 4884.442
## Bayesian (BIC) 4954.169
## Sample-size adjusted Bayesian (SABIC) 4878.249
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.081
## 90 Percent confidence interval - lower 0.048
## 90 Percent confidence interval - upper 0.113
## P-value H_0: RMSEA <= 0.050 0.057
## P-value H_0: RMSEA >= 0.080 0.553
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.067
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## BMSi ~
## milk (i) 1.854 0.925 2.005 0.045 0.042 3.667
## age_final -0.193 0.108 -1.794 0.073 -0.404 0.018
## female_b2 -0.056 1.603 -0.035 0.972 -3.197 3.086
## PA_SCORE_2 0.173 0.118 1.468 0.142 -0.058 0.404
## vitd_top -0.072 0.124 -0.578 0.564 -0.316 0.172
## BMI_b2 -0.274 0.125 -2.190 0.029 -0.520 -0.029
## alchl_fr_8 -0.154 1.272 -0.121 0.904 -2.646 2.339
## IL6 ~
## milk (a) -0.613 0.522 -1.174 0.240 -1.636 0.410
## diabts_bn2 -0.430 0.834 -0.515 0.606 -2.065 1.206
## TNFa ~
## milk (c) 0.770 0.794 0.970 0.332 -0.787 2.327
## diabts_bn2 1.568 1.270 1.234 0.217 -0.922 4.057
## IL1B ~
## milk (e) -1.630 2.986 -0.546 0.585 -7.482 4.223
## diabts_bn2 -5.674 4.774 -1.189 0.235 -15.031 3.683
## CRP ~
## milk (g) -1.569 0.702 -2.234 0.025 -2.945 -0.192
## diabts_bn2 1.145 1.123 1.020 0.308 -1.055 3.345
## BMSi ~
## IL6 (b) -0.165 0.138 -1.191 0.234 -0.435 0.106
## TNFa (d) -0.056 0.090 -0.623 0.533 -0.234 0.121
## IL1B (f) -0.027 0.024 -1.130 0.259 -0.074 0.020
## CRP (h) -0.003 0.102 -0.031 0.975 -0.204 0.198
## Std.lv Std.all
##
## 1.854 0.179
## -0.193 -0.154
## -0.056 -0.003
## 0.173 0.124
## -0.072 -0.049
## -0.274 -0.188
## -0.154 -0.010
##
## -0.613 -0.101
## -0.430 -0.044
##
## 0.770 0.083
## 1.568 0.105
##
## -1.630 -0.047
## -5.674 -0.102
##
## -1.569 -0.188
## 1.145 0.086
##
## -0.165 -0.097
## -0.056 -0.051
## -0.027 -0.092
## -0.003 -0.003
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## .BMSi 60.451 7.358 8.216 0.000 46.030 74.872
## .IL6 23.406 2.849 8.216 0.000 17.822 28.990
## .TNFa 54.234 6.601 8.216 0.000 41.296 67.172
## .IL1B 766.231 93.263 8.216 0.000 583.440 949.022
## .CRP 42.373 5.157 8.216 0.000 32.264 52.481
## Std.lv Std.all
## 60.451 0.889
## 23.406 0.988
## 54.234 0.983
## 766.231 0.988
## 42.373 0.956
##
## Defined Parameters:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## ab 0.101 0.121 0.836 0.403 -0.136 0.337
## cd -0.043 0.083 -0.524 0.600 -0.206 0.119
## ef 0.044 0.090 0.491 0.623 -0.132 0.221
## gh 0.005 0.161 0.031 0.975 -0.310 0.320
## total 1.961 0.912 2.150 0.032 0.174 3.748
## Std.lv Std.all
## 0.101 0.010
## -0.043 -0.004
## 0.044 0.004
## 0.005 0.000
## 1.961 0.190semPaths(fit_milk_adj)
Adjusted milk with log tranformed mediators(without this tranformation, the variances are extremely high)
model_milk_adj_log <- ' # direct effect
BMSi ~ i*milk + age_final + female_b2 + PA_SCORE_b2 + vitd_top + BMI_b2 + alcohol_freq_8yr
# mediator
log_IL6 ~ a*milk + diabetes_bone2
log_tnf ~ c*milk + diabetes_bone2
log_il1B ~ e*milk + diabetes_bone2
log_crp ~ g*milk + diabetes_bone2
BMSi ~ b*log_IL6
BMSi ~ d*log_tnf
BMSi ~ f*log_il1B
BMSi ~ h*log_crp
# indirect effect (a*b)
ab := a*b
cd := c*d
ef := e*f
gh := g*h
# total effect
total := i + (a*b) +(c*d) +(e*f) +(g*h)
'
fit_milk_adj_log <- sem(model_milk_adj_log, data = db)
summary(fit_milk_adj_log, fit.measures=TRUE, standardized=TRUE, ci=TRUE)## lavaan 0.6-18 ended normally after 1 iteration
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 24
##
## Used Total
## Number of observations 135 163
##
## Model Test User Model:
##
## Test statistic 53.804
## Degrees of freedom 31
## P-value (Chi-square) 0.007
##
## Model Test Baseline Model:
##
## Test statistic 89.444
## Degrees of freedom 50
## P-value 0.001
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.422
## Tucker-Lewis Index (TLI) 0.068
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -1158.566
## Loglikelihood unrestricted model (H1) -1131.664
##
## Akaike (AIC) 2365.133
## Bayesian (BIC) 2434.859
## Sample-size adjusted Bayesian (SABIC) 2358.939
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.074
## 90 Percent confidence interval - lower 0.039
## 90 Percent confidence interval - upper 0.106
## P-value H_0: RMSEA <= 0.050 0.117
## P-value H_0: RMSEA >= 0.080 0.404
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.068
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## BMSi ~
## milk (i) 1.811 0.911 1.988 0.047 0.025 3.596
## age_final -0.216 0.105 -2.048 0.041 -0.422 -0.009
## female_b2 0.260 1.566 0.166 0.868 -2.810 3.330
## PA_SCORE_2 0.209 0.115 1.818 0.069 -0.016 0.435
## vitd_top -0.055 0.122 -0.454 0.650 -0.293 0.183
## BMI_b2 -0.317 0.122 -2.590 0.010 -0.557 -0.077
## alchl_fr_8 -0.532 1.243 -0.428 0.668 -2.968 1.903
## log_IL6 ~
## milk (a) -0.158 0.100 -1.584 0.113 -0.354 0.038
## diabts_bn2 -0.066 0.160 -0.416 0.678 -0.379 0.246
## log_tnf ~
## milk (c) 0.061 0.056 1.092 0.275 -0.049 0.171
## diabts_bn2 0.151 0.090 1.688 0.091 -0.024 0.327
## log_il1B ~
## milk (e) -0.145 0.100 -1.447 0.148 -0.341 0.051
## diabts_bn2 -0.187 0.160 -1.168 0.243 -0.501 0.127
## log_crp ~
## milk (g) -0.304 0.141 -2.159 0.031 -0.580 -0.028
## diabts_bn2 0.035 0.225 0.154 0.877 -0.407 0.476
## BMSi ~
## log_IL6 (b) -1.630 0.706 -2.308 0.021 -3.014 -0.246
## log_tnf (d) -1.040 1.246 -0.835 0.404 -3.483 1.402
## log_il1B (f) -1.136 0.701 -1.619 0.105 -2.511 0.239
## log_crp (h) 0.828 0.501 1.652 0.098 -0.154 1.809
## Std.lv Std.all
##
## 1.811 0.172
## -0.216 -0.169
## 0.260 0.014
## 0.209 0.147
## -0.055 -0.037
## -0.317 -0.214
## -0.532 -0.035
##
## -0.158 -0.135
## -0.066 -0.035
##
## 0.061 0.093
## 0.151 0.143
##
## -0.145 -0.123
## -0.187 -0.099
##
## -0.304 -0.183
## 0.035 0.013
##
## -1.630 -0.182
## -1.040 -0.065
## -1.136 -0.127
## 0.828 0.131
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## .BMSi 57.719 7.025 8.216 0.000 43.950 71.489
## .log_IL6 0.856 0.104 8.216 0.000 0.652 1.060
## .log_tnf 0.270 0.033 8.216 0.000 0.206 0.335
## .log_il1B 0.861 0.105 8.216 0.000 0.656 1.066
## .log_crp 1.704 0.207 8.216 0.000 1.297 2.110
## Std.lv Std.all
## 57.719 0.821
## 0.856 0.981
## 0.270 0.972
## 0.861 0.976
## 1.704 0.966
##
## Defined Parameters:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## ab 0.258 0.197 1.306 0.192 -0.129 0.644
## cd -0.064 0.096 -0.663 0.507 -0.252 0.125
## ef 0.164 0.152 1.079 0.281 -0.134 0.463
## gh -0.252 0.192 -1.312 0.189 -0.628 0.124
## total 1.918 0.914 2.098 0.036 0.126 3.709
## Std.lv Std.all
## 0.258 0.025
## -0.064 -0.006
## 0.164 0.016
## -0.252 -0.024
## 1.918 0.183semPaths(fit_milk_adj_log)
Fluid dairy adjusted
model_fluid_adj <- ' # direct effect
BMSi ~ i*fluid + age_final + female_b2 + PA_SCORE_b2 + vitd_top + BMI_b2 + alcohol_freq_8yr
# mediator
IL6 ~ a*fluid + diabetes_bone2
TNFa ~ c*fluid + diabetes_bone2
IL1B ~ e*fluid + diabetes_bone2
CRP ~ g*fluid + diabetes_bone2
BMSi ~ b*IL6
BMSi ~ d*TNFa
BMSi ~ f*IL1B
BMSi ~ h*CRP
# indirect effect (a*b)
ab := a*b
cd := c*d
ef := e*f
gh := g*h
# total effect
total := i + (a*b) +(c*d) +(e*f) +(g*h)
'
fit_fluid_adj <- sem(model_fluid_adj, data = db)
summary(fit_fluid_adj, fit.measures=TRUE, standardized=TRUE, ci=TRUE)## lavaan 0.6-18 ended normally after 1 iteration
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 24
##
## Used Total
## Number of observations 135 163
##
## Model Test User Model:
##
## Test statistic 58.940
## Degrees of freedom 31
## P-value (Chi-square) 0.002
##
## Model Test Baseline Model:
##
## Test statistic 85.243
## Degrees of freedom 50
## P-value 0.001
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.207
## Tucker-Lewis Index (TLI) -0.279
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -2418.397
## Loglikelihood unrestricted model (H1) -2388.927
##
## Akaike (AIC) 4884.794
## Bayesian (BIC) 4954.521
## Sample-size adjusted Bayesian (SABIC) 4878.601
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.082
## 90 Percent confidence interval - lower 0.049
## 90 Percent confidence interval - upper 0.113
## P-value H_0: RMSEA <= 0.050 0.055
## P-value H_0: RMSEA >= 0.080 0.562
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.067
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## BMSi ~
## fluid (i) 1.733 0.872 1.988 0.047 0.024 3.442
## age_final -0.196 0.108 -1.817 0.069 -0.408 0.015
## female_b2 -0.154 1.609 -0.096 0.924 -3.307 2.998
## PA_SCORE_2 0.170 0.118 1.445 0.148 -0.061 0.401
## vitd_top -0.075 0.125 -0.598 0.550 -0.319 0.170
## BMI_b2 -0.278 0.125 -2.222 0.026 -0.524 -0.033
## alchl_fr_8 -0.135 1.274 -0.106 0.915 -2.633 2.362
## IL6 ~
## fluid (a) -0.546 0.489 -1.118 0.264 -1.504 0.412
## diabts_bn2 -0.443 0.835 -0.530 0.596 -2.080 1.195
## TNFa ~
## fluid (c) 0.777 0.743 1.045 0.296 -0.680 2.233
## diabts_bn2 1.591 1.270 1.253 0.210 -0.898 4.081
## IL1B ~
## fluid (e) -1.519 2.795 -0.543 0.587 -6.996 3.959
## diabts_bn2 -5.714 4.777 -1.196 0.232 -15.077 3.649
## CRP ~
## fluid (g) -1.424 0.658 -2.165 0.030 -2.714 -0.135
## diabts_bn2 1.110 1.125 0.987 0.324 -1.094 3.314
## BMSi ~
## IL6 (b) -0.166 0.138 -1.199 0.230 -0.437 0.105
## TNFa (d) -0.057 0.090 -0.635 0.526 -0.235 0.120
## IL1B (f) -0.028 0.024 -1.143 0.253 -0.075 0.020
## CRP (h) -0.004 0.102 -0.035 0.972 -0.204 0.197
## Std.lv Std.all
##
## 1.733 0.179
## -0.196 -0.157
## -0.154 -0.008
## 0.170 0.122
## -0.075 -0.051
## -0.278 -0.191
## -0.135 -0.009
##
## -0.546 -0.096
## -0.443 -0.045
##
## 0.777 0.089
## 1.591 0.107
##
## -1.519 -0.047
## -5.714 -0.102
##
## -1.424 -0.183
## 1.110 0.083
##
## -0.166 -0.098
## -0.057 -0.052
## -0.028 -0.093
## -0.004 -0.003
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## .BMSi 60.485 7.362 8.216 0.000 46.056 74.915
## .IL6 23.428 2.852 8.216 0.000 17.839 29.017
## .TNFa 54.173 6.594 8.216 0.000 41.250 67.097
## .IL1B 766.246 93.264 8.216 0.000 583.451 949.041
## .CRP 42.465 5.169 8.216 0.000 32.335 52.596
## Std.lv Std.all
## 60.485 0.889
## 23.428 0.989
## 54.173 0.982
## 766.246 0.988
## 42.465 0.958
##
## Defined Parameters:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## ab 0.090 0.111 0.818 0.414 -0.126 0.307
## cd -0.045 0.082 -0.542 0.587 -0.206 0.117
## ef 0.042 0.085 0.491 0.624 -0.125 0.209
## gh 0.005 0.146 0.035 0.972 -0.281 0.291
## total 1.826 0.861 2.121 0.034 0.139 3.514
## Std.lv Std.all
## 0.090 0.009
## -0.045 -0.005
## 0.042 0.004
## 0.005 0.001
## 1.826 0.189semPaths(fit_fluid_adj)
Fluid dairy adjusted w/ log transformed mediators
model_fluid_adj_log <- ' # direct effect
BMSi ~ i*fluid + age_final + female_b2 + PA_SCORE_b2 + vitd_top + BMI_b2 + alcohol_freq_8yr
# mediator
log_IL6 ~ a*fluid + diabetes_bone2
log_tnf ~ c*fluid + diabetes_bone2
log_il1B ~ e*fluid + diabetes_bone2
log_crp ~ g*fluid + diabetes_bone2
BMSi ~ b*log_IL6
BMSi ~ d*log_tnf
BMSi ~ f*log_il1B
BMSi ~ h*log_crp
# indirect effect (a*b)
ab := a*b
cd := c*d
ef := e*f
gh := g*h
# total effect
total := i + (a*b) +(c*d) +(e*f) +(g*h)
'
fit_fluid_adj_log <- sem(model_fluid_adj_log, data = db)
summary(fit_fluid_adj_log, fit.measures=TRUE, standardized=TRUE, ci=TRUE)## lavaan 0.6-18 ended normally after 1 iteration
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 24
##
## Used Total
## Number of observations 135 163
##
## Model Test User Model:
##
## Test statistic 54.397
## Degrees of freedom 31
## P-value (Chi-square) 0.006
##
## Model Test Baseline Model:
##
## Test statistic 89.182
## Degrees of freedom 50
## P-value 0.001
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.403
## Tucker-Lewis Index (TLI) 0.037
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -1158.994
## Loglikelihood unrestricted model (H1) -1131.795
##
## Akaike (AIC) 2365.988
## Bayesian (BIC) 2435.714
## Sample-size adjusted Bayesian (SABIC) 2359.794
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.075
## 90 Percent confidence interval - lower 0.040
## 90 Percent confidence interval - upper 0.107
## P-value H_0: RMSEA <= 0.050 0.108
## P-value H_0: RMSEA >= 0.080 0.422
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.069
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## BMSi ~
## fluid (i) 1.730 0.856 2.021 0.043 0.052 3.407
## age_final -0.220 0.105 -2.084 0.037 -0.426 -0.013
## female_b2 0.158 1.571 0.100 0.920 -2.921 3.237
## PA_SCORE_2 0.207 0.115 1.804 0.071 -0.018 0.432
## vitd_top -0.059 0.122 -0.482 0.630 -0.297 0.180
## BMI_b2 -0.321 0.122 -2.628 0.009 -0.561 -0.082
## alchl_fr_8 -0.505 1.244 -0.406 0.685 -2.943 1.934
## log_IL6 ~
## fluid (a) -0.130 0.094 -1.391 0.164 -0.314 0.053
## diabts_bn2 -0.069 0.160 -0.429 0.668 -0.382 0.245
## log_tnf ~
## fluid (c) 0.064 0.052 1.226 0.220 -0.038 0.167
## diabts_bn2 0.153 0.090 1.712 0.087 -0.022 0.329
## log_il1B ~
## fluid (e) -0.122 0.094 -1.303 0.193 -0.306 0.062
## diabts_bn2 -0.189 0.160 -1.181 0.238 -0.504 0.125
## log_crp ~
## fluid (g) -0.275 0.132 -2.082 0.037 -0.533 -0.016
## diabts_bn2 0.028 0.226 0.124 0.901 -0.414 0.470
## BMSi ~
## log_IL6 (b) -1.641 0.704 -2.330 0.020 -3.022 -0.261
## log_tnf (d) -1.072 1.247 -0.860 0.390 -3.516 1.372
## log_il1B (f) -1.163 0.700 -1.661 0.097 -2.535 0.209
## log_crp (h) 0.832 0.500 1.664 0.096 -0.148 1.813
## Std.lv Std.all
##
## 1.730 0.176
## -0.220 -0.172
## 0.158 0.008
## 0.207 0.146
## -0.059 -0.040
## -0.321 -0.217
## -0.505 -0.033
##
## -0.130 -0.119
## -0.069 -0.037
##
## 0.064 0.104
## 0.153 0.145
##
## -0.122 -0.111
## -0.189 -0.101
##
## -0.275 -0.177
## 0.028 0.011
##
## -1.641 -0.183
## -1.072 -0.067
## -1.163 -0.130
## 0.832 0.132
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## .BMSi 57.673 7.020 8.216 0.000 43.914 71.431
## .log_IL6 0.860 0.105 8.216 0.000 0.655 1.065
## .log_tnf 0.269 0.033 8.216 0.000 0.205 0.334
## .log_il1B 0.864 0.105 8.216 0.000 0.658 1.070
## .log_crp 1.708 0.208 8.216 0.000 1.300 2.115
## Std.lv Std.all
## 57.673 0.820
## 0.860 0.985
## 0.269 0.970
## 0.864 0.979
## 1.708 0.969
##
## Defined Parameters:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## ab 0.214 0.179 1.194 0.232 -0.137 0.565
## cd -0.069 0.098 -0.704 0.481 -0.261 0.123
## ef 0.142 0.139 1.025 0.305 -0.130 0.414
## gh -0.229 0.176 -1.300 0.194 -0.573 0.116
## total 1.788 0.863 2.073 0.038 0.098 3.479
## Std.lv Std.all
## 0.214 0.022
## -0.069 -0.007
## 0.142 0.014
## -0.229 -0.023
## 1.788 0.182semPaths(fit_fluid_adj_log)
Total dairy adjusted
model_total_adj <- ' # direct effect
BMSi ~ i*mod + age_final + female_b2 + PA_SCORE_b2 + vitd_top + BMI_b2 + alcohol_freq_8yr
# mediator
IL6 ~ a*mod + diabetes_bone2
TNFa ~ c*mod + diabetes_bone2
IL1B ~ e*mod + diabetes_bone2
CRP ~ g*mod + diabetes_bone2
BMSi ~ b*IL6
BMSi ~ d*TNFa
BMSi ~ f*IL1B
BMSi ~ h*CRP
# indirect effect (a*b)
ab := a*b
cd := c*d
ef := e*f
gh := g*h
# total effect
total := i + (a*b) +(c*d) +(e*f) +(g*h)
'
fit_total_adj <- sem(model_total_adj, data = db)
summary(fit_total_adj,fit.measures=TRUE, standardized=TRUE, ci=TRUE)## lavaan 0.6-18 ended normally after 1 iteration
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 24
##
## Used Total
## Number of observations 135 163
##
## Model Test User Model:
##
## Test statistic 57.896
## Degrees of freedom 31
## P-value (Chi-square) 0.002
##
## Model Test Baseline Model:
##
## Test statistic 84.737
## Degrees of freedom 50
## P-value 0.002
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.226
## Tucker-Lewis Index (TLI) -0.249
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -2418.128
## Loglikelihood unrestricted model (H1) -2389.180
##
## Akaike (AIC) 4884.256
## Bayesian (BIC) 4953.983
## Sample-size adjusted Bayesian (SABIC) 4878.062
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.080
## 90 Percent confidence interval - lower 0.047
## 90 Percent confidence interval - upper 0.112
## P-value H_0: RMSEA <= 0.050 0.064
## P-value H_0: RMSEA >= 0.080 0.530
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.066
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## BMSi ~
## mod (i) 1.817 0.885 2.052 0.040 0.081 3.552
## age_final -0.189 0.107 -1.767 0.077 -0.400 0.021
## female_b2 -0.232 1.612 -0.144 0.886 -3.391 2.928
## PA_SCORE_2 0.162 0.117 1.382 0.167 -0.068 0.391
## vitd_top -0.087 0.126 -0.693 0.488 -0.333 0.159
## BMI_b2 -0.270 0.125 -2.154 0.031 -0.515 -0.024
## alchl_fr_8 -0.082 1.276 -0.064 0.949 -2.584 2.420
## IL6 ~
## mod (a) -0.473 0.493 -0.959 0.337 -1.440 0.494
## diabts_bn2 -0.441 0.837 -0.527 0.598 -2.081 1.199
## TNFa ~
## mod (c) 0.535 0.751 0.712 0.476 -0.937 2.006
## diabts_bn2 1.576 1.273 1.237 0.216 -0.920 4.071
## IL1B ~
## mod (e) -1.622 2.817 -0.576 0.565 -7.144 3.899
## diabts_bn2 -5.738 4.778 -1.201 0.230 -15.102 3.627
## CRP ~
## mod (g) -1.599 0.661 -2.421 0.015 -2.894 -0.305
## diabts_bn2 1.080 1.120 0.964 0.335 -1.115 3.276
## BMSi ~
## IL6 (b) -0.171 0.138 -1.238 0.216 -0.441 0.099
## TNFa (d) -0.052 0.090 -0.573 0.566 -0.228 0.125
## IL1B (f) -0.027 0.024 -1.114 0.265 -0.074 0.020
## CRP (h) -0.002 0.103 -0.017 0.986 -0.203 0.200
## Std.lv Std.all
##
## 1.817 0.187
## -0.189 -0.151
## -0.232 -0.012
## 0.162 0.116
## -0.087 -0.060
## -0.270 -0.185
## -0.082 -0.005
##
## -0.473 -0.082
## -0.441 -0.045
##
## 0.535 0.061
## 1.576 0.106
##
## -1.622 -0.049
## -5.738 -0.103
##
## -1.599 -0.203
## 1.080 0.081
##
## -0.171 -0.101
## -0.052 -0.047
## -0.027 -0.090
## -0.002 -0.001
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## .BMSi 60.362 7.347 8.216 0.000 45.962 74.761
## .IL6 23.485 2.858 8.216 0.000 17.882 29.088
## .TNFa 54.407 6.622 8.216 0.000 41.428 67.386
## .IL1B 766.040 93.239 8.216 0.000 583.294 948.785
## .CRP 42.110 5.125 8.216 0.000 32.064 52.156
## Std.lv Std.all
## 60.362 0.887
## 23.485 0.992
## 54.407 0.986
## 766.040 0.988
## 42.110 0.950
##
## Defined Parameters:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## ab 0.081 0.107 0.758 0.448 -0.128 0.290
## cd -0.028 0.062 -0.447 0.655 -0.149 0.094
## ef 0.043 0.085 0.512 0.609 -0.123 0.210
## gh 0.003 0.164 0.017 0.986 -0.319 0.325
## total 1.916 0.873 2.194 0.028 0.204 3.628
## Std.lv Std.all
## 0.081 0.008
## -0.028 -0.003
## 0.043 0.004
## 0.003 0.000
## 1.916 0.197semPaths(fit_total_adj)
##total adjusted with log transformed mediators
model_total_adj_log <- ' # direct effect
BMSi ~ i*mod + age_final + female_b2 + PA_SCORE_b2 + vitd_top + BMI_b2 + alcohol_freq_8yr
# mediator
log_IL6 ~ a*mod + diabetes_bone2
log_tnf ~ c*mod + diabetes_bone2
log_il1B ~ e*mod + diabetes_bone2
log_crp ~ g*mod + diabetes_bone2
BMSi ~ b*log_IL6
BMSi ~ d*log_tnf
BMSi ~ f*log_il1B
BMSi ~ h*log_crp
# indirect effect (a*b)
ab := a*b
cd := c*d
ef := e*f
gh := g*h
# total effect
total := i + (a*b) +(c*d) +(e*f) +(g*h)
'
fit_total_adj_log <- sem(model_total_adj_log, data = db)
summary(fit_total_adj_log,fit.measures=TRUE, standardized=TRUE, ci=TRUE)## lavaan 0.6-18 ended normally after 1 iteration
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 24
##
## Used Total
## Number of observations 135 163
##
## Model Test User Model:
##
## Test statistic 53.392
## Degrees of freedom 31
## P-value (Chi-square) 0.007
##
## Model Test Baseline Model:
##
## Test statistic 89.359
## Degrees of freedom 50
## P-value 0.001
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.431
## Tucker-Lewis Index (TLI) 0.082
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -1158.403
## Loglikelihood unrestricted model (H1) -1131.707
##
## Akaike (AIC) 2364.805
## Bayesian (BIC) 2434.532
## Sample-size adjusted Bayesian (SABIC) 2358.612
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.073
## 90 Percent confidence interval - lower 0.038
## 90 Percent confidence interval - upper 0.106
## P-value H_0: RMSEA <= 0.050 0.124
## P-value H_0: RMSEA >= 0.080 0.391
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.068
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## BMSi ~
## mod (i) 1.796 0.871 2.062 0.039 0.089 3.504
## age_final -0.211 0.105 -2.019 0.043 -0.417 -0.006
## female_b2 0.068 1.575 0.043 0.965 -3.018 3.155
## PA_SCORE_2 0.198 0.114 1.736 0.082 -0.026 0.423
## vitd_top -0.070 0.123 -0.573 0.567 -0.311 0.170
## BMI_b2 -0.312 0.122 -2.553 0.011 -0.552 -0.073
## alchl_fr_8 -0.458 1.247 -0.368 0.713 -2.902 1.985
## log_IL6 ~
## mod (a) -0.130 0.094 -1.381 0.167 -0.315 0.055
## diabts_bn2 -0.070 0.160 -0.437 0.662 -0.384 0.244
## log_tnf ~
## mod (c) 0.055 0.053 1.036 0.300 -0.049 0.159
## diabts_bn2 0.153 0.090 1.705 0.088 -0.023 0.329
## log_il1B ~
## mod (e) -0.131 0.095 -1.391 0.164 -0.317 0.054
## diabts_bn2 -0.191 0.160 -1.194 0.233 -0.505 0.123
## log_crp ~
## mod (g) -0.313 0.132 -2.366 0.018 -0.573 -0.054
## diabts_bn2 0.022 0.225 0.097 0.922 -0.418 0.462
## BMSi ~
## log_IL6 (b) -1.638 0.704 -2.327 0.020 -3.018 -0.258
## log_tnf (d) -1.035 1.244 -0.832 0.405 -3.474 1.403
## log_il1B (f) -1.137 0.700 -1.624 0.104 -2.509 0.235
## log_crp (h) 0.837 0.502 1.667 0.096 -0.147 1.821
## Std.lv Std.all
##
## 1.796 0.182
## -0.211 -0.166
## 0.068 0.004
## 0.198 0.140
## -0.070 -0.048
## -0.312 -0.211
## -0.458 -0.030
##
## -0.130 -0.118
## -0.070 -0.037
##
## 0.055 0.088
## 0.153 0.145
##
## -0.131 -0.119
## -0.191 -0.102
##
## -0.313 -0.200
## 0.022 0.008
##
## -1.638 -0.183
## -1.035 -0.065
## -1.137 -0.127
## 0.837 0.133
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## .BMSi 57.594 7.010 8.216 0.000 43.854 71.333
## .log_IL6 0.860 0.105 8.216 0.000 0.655 1.065
## .log_tnf 0.270 0.033 8.216 0.000 0.206 0.335
## .log_il1B 0.862 0.105 8.216 0.000 0.656 1.068
## .log_crp 1.693 0.206 8.216 0.000 1.289 2.096
## Std.lv Std.all
## 57.594 0.820
## 0.860 0.985
## 0.270 0.973
## 0.862 0.977
## 1.693 0.960
##
## Defined Parameters:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## ab 0.214 0.180 1.188 0.235 -0.139 0.566
## cd -0.057 0.087 -0.649 0.517 -0.228 0.115
## ef 0.149 0.141 1.056 0.291 -0.128 0.427
## gh -0.262 0.192 -1.363 0.173 -0.639 0.115
## total 1.841 0.875 2.104 0.035 0.126 3.555
## Std.lv Std.all
## 0.214 0.022
## -0.057 -0.006
## 0.149 0.015
## -0.262 -0.026
## 1.841 0.186semPaths(fit_total_adj_log)
No-fat as predictor var, TBS as response var; IL6, TNFa, IL1B, CRP as individual mediators
model_skim_TBS <- ' # direct effect
TBSL1L2L3L4_final ~ i*skim
# mediator
IL6 ~ a*skim
TNFa ~ c*skim
IL1B ~ e*skim
CRP ~ g*skim
TBSL1L2L3L4_final ~ b*IL6
TBSL1L2L3L4_final ~ d*TNFa
TBSL1L2L3L4_final ~ f*IL1B
TBSL1L2L3L4_final ~ h*CRP
# indirect effect (a*b)
ab := a*b
cd := c*d
ef := e*f
gh := g*h
# total effect
total := i + (a*b) +(c*d) +(e*f) +(g*h)
'
fit2 <- sem(model_skim_TBS, data = db2)## Warning: lavaan->lav_data_full():
## some observed variances are (at least) a factor 1000 times larger than
## others; use varTable(fit) to investigatesummary(fit2,fit.measures=TRUE, standardized=TRUE, ci=TRUE )## lavaan 0.6-18 ended normally after 34 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 14
##
## Used Total
## Number of observations 396 445
##
## Model Test User Model:
##
## Test statistic 81.283
## Degrees of freedom 6
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 93.077
## Degrees of freedom 15
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.036
## Tucker-Lewis Index (TLI) -1.411
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -5940.723
## Loglikelihood unrestricted model (H1) -5900.081
##
## Akaike (AIC) 11909.445
## Bayesian (BIC) 11965.185
## Sample-size adjusted Bayesian (SABIC) 11920.763
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.178
## 90 Percent confidence interval - lower 0.145
## 90 Percent confidence interval - upper 0.213
## P-value H_0: RMSEA <= 0.050 0.000
## P-value H_0: RMSEA >= 0.080 1.000
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.099
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## TBSL1L2L3L4_final ~
## skim (i) -0.046 0.018 -2.518 0.012 -0.081 -0.010
## IL6 ~
## skim (a) 0.642 0.693 0.927 0.354 -0.716 2.000
## TNFa ~
## skim (c) 0.241 0.871 0.277 0.782 -1.466 1.948
## IL1B ~
## skim (e) 0.231 4.620 0.050 0.960 -8.824 9.287
## CRP ~
## skim (g) -1.894 1.344 -1.409 0.159 -4.528 0.741
## TBSL1L2L3L4_final ~
## IL6 (b) 0.000 0.001 0.314 0.753 -0.002 0.003
## TNFa (d) -0.001 0.001 -0.567 0.571 -0.003 0.001
## IL1B (f) 0.000 0.000 1.465 0.143 -0.000 0.001
## CRP (h) -0.000 0.001 -0.647 0.518 -0.002 0.001
## Std.lv Std.all
##
## -0.046 -0.126
##
## 0.642 0.047
##
## 0.241 0.014
##
## 0.231 0.003
##
## -1.894 -0.071
##
## 0.000 0.016
## -0.001 -0.028
## 0.000 0.073
## -0.000 -0.032
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## .TBSL1L2L3L4_fn 0.023 0.002 14.071 0.000 0.020 0.026
## .IL6 33.309 2.367 14.071 0.000 28.669 37.949
## .TNFa 52.641 3.741 14.071 0.000 45.308 59.973
## .IL1B 1481.066 105.255 14.071 0.000 1274.770 1687.361
## .CRP 125.373 8.910 14.071 0.000 107.910 142.836
## Std.lv Std.all
## 0.023 0.978
## 33.309 0.998
## 52.641 1.000
## 1481.066 1.000
## 125.373 0.995
##
## Defined Parameters:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## ab 0.000 0.001 0.298 0.766 -0.001 0.002
## cd -0.000 0.001 -0.249 0.804 -0.001 0.001
## ef 0.000 0.001 0.050 0.960 -0.003 0.003
## gh 0.001 0.001 0.588 0.557 -0.002 0.004
## total -0.045 0.018 -2.462 0.014 -0.080 -0.009
## Std.lv Std.all
## 0.000 0.001
## -0.000 -0.000
## 0.000 0.000
## 0.001 0.002
## -0.045 -0.123semPaths(fit2)
#Adjusted skim
model_skim_adj_TBS <- ' # direct effect
TBSL1L2L3L4_final ~ i*skim + age_final + female_b2 + PA_SCORE_b2 + vitd_top + BMI_b2 + alcohol_freq_8yr
# mediator
IL6 ~ a*skim + diabetes_bone2
TNFa ~ c*skim + diabetes_bone2
IL1B ~ e*skim + diabetes_bone2
CRP ~ g*skim + diabetes_bone2
TBSL1L2L3L4_final ~ b*IL6
TBSL1L2L3L4_final ~ d*TNFa
TBSL1L2L3L4_final ~ f*IL1B
TBSL1L2L3L4_final ~ h*CRP
# indirect effect (a*b)
ab := a*b
cd := c*d
ef := e*f
gh := g*h
# total effect
total := i + (a*b) +(c*d) +(e*f) +(g*h)
'
fit2_adj <- sem(model_skim_adj_TBS, data = db2)## Warning: lavaan->lav_data_full():
## some observed variances are (at least) a factor 1000 times larger than
## others; use varTable(fit) to investigatesummary(fit2_adj,fit.measures=TRUE, standardized=TRUE, ci=TRUE )## lavaan 0.6-18 ended normally after 1 iteration
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 24
##
## Used Total
## Number of observations 362 445
##
## Model Test User Model:
##
## Test statistic 105.593
## Degrees of freedom 31
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 133.730
## Degrees of freedom 50
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.109
## Tucker-Lewis Index (TLI) -0.437
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -5446.680
## Loglikelihood unrestricted model (H1) NA
##
## Akaike (AIC) 10941.359
## Bayesian (BIC) 11034.759
## Sample-size adjusted Bayesian (SABIC) 10958.618
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.082
## 90 Percent confidence interval - lower 0.065
## 90 Percent confidence interval - upper 0.099
## P-value H_0: RMSEA <= 0.050 0.001
## P-value H_0: RMSEA >= 0.080 0.578
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.058
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## TBSL1L2L3L4_final ~
## skim (i) -0.045 0.019 -2.409 0.016 -0.082 -0.008
## age_final -0.001 0.001 -0.452 0.652 -0.003 0.002
## female_b2 -0.017 0.020 -0.875 0.381 -0.055 0.021
## PA_SCORE_2 0.000 0.001 0.137 0.891 -0.002 0.003
## vitd_top -0.000 0.001 -0.313 0.754 -0.003 0.002
## BMI_b2 -0.002 0.001 -1.912 0.056 -0.005 0.000
## alchl_fr_8 0.003 0.015 0.217 0.828 -0.027 0.033
## IL6 ~
## skim (a) 0.529 0.743 0.711 0.477 -0.929 1.986
## diabts_bn2 0.789 0.645 1.224 0.221 -0.475 2.053
## TNFa ~
## skim (c) 0.116 0.919 0.126 0.900 -1.686 1.917
## diabts_bn2 1.541 0.797 1.934 0.053 -0.021 3.103
## IL1B ~
## skim (e) 2.011 4.616 0.436 0.663 -7.035 11.057
## diabts_bn2 -6.216 4.003 -1.553 0.120 -14.061 1.629
## CRP ~
## skim (g) -2.216 1.415 -1.566 0.117 -4.988 0.557
## diabts_bn2 2.382 1.227 1.942 0.052 -0.022 4.787
## TBSL1L2L3L4_final ~
## IL6 (b) 0.000 0.001 0.296 0.767 -0.002 0.003
## TNFa (d) -0.001 0.001 -0.564 0.573 -0.003 0.001
## IL1B (f) 0.000 0.000 1.130 0.259 -0.000 0.001
## CRP (h) -0.000 0.001 -0.215 0.830 -0.002 0.001
## Std.lv Std.all
##
## -0.045 -0.125
## -0.001 -0.024
## -0.017 -0.047
## 0.000 0.007
## -0.000 -0.016
## -0.002 -0.104
## 0.003 0.011
##
## 0.529 0.038
## 0.789 0.065
##
## 0.116 0.007
## 1.541 0.102
##
## 2.011 0.023
## -6.216 -0.082
##
## -2.216 -0.082
## 2.382 0.102
##
## 0.000 0.015
## -0.001 -0.029
## 0.000 0.058
## -0.000 -0.011
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## .TBSL1L2L3L4_fn 0.023 0.002 13.454 0.000 0.020 0.026
## .IL6 35.848 2.665 13.454 0.000 30.625 41.070
## .TNFa 54.779 4.072 13.454 0.000 46.799 62.760
## .IL1B 1381.734 102.703 13.454 0.000 1180.439 1583.029
## .CRP 129.789 9.647 13.454 0.000 110.881 148.697
## Std.lv Std.all
## 0.023 0.963
## 35.848 0.994
## 54.779 0.989
## 1381.734 0.993
## 129.789 0.985
##
## Defined Parameters:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## ab 0.000 0.001 0.273 0.785 -0.001 0.002
## cd -0.000 0.001 -0.123 0.902 -0.001 0.001
## ef 0.000 0.001 0.406 0.684 -0.002 0.003
## gh 0.000 0.002 0.213 0.831 -0.003 0.003
## total -0.044 0.019 -2.361 0.018 -0.081 -0.008
## Std.lv Std.all
## 0.000 0.001
## -0.000 -0.000
## 0.000 0.001
## 0.000 0.001
## -0.044 -0.123semPaths(fit2_adj)
skim & tbs adjusted with log tranformed inflammatory cytokines
model_skim_TBS_log <- ' # direct effect
TBSL1L2L3L4_final ~ i*skim + age_final + female_b2 + PA_SCORE_b2 + vitd_top + BMI_b2 + alcohol_freq_8yr
# mediator
log_IL6 ~ a*skim + diabetes_bone2
log_tnf ~ c*skim + diabetes_bone2
log_il1B ~ e*skim + diabetes_bone2
log_crp ~ g*skim + diabetes_bone2
TBSL1L2L3L4_final ~ b*log_IL6
TBSL1L2L3L4_final ~ d*log_tnf
TBSL1L2L3L4_final ~ f*log_il1B
TBSL1L2L3L4_final ~ h*log_crp
# indirect effect (a*b)
ab := a*b
cd := c*d
ef := e*f
# total effect
total := i + (a*b) +(c*d) +(e*f) +(g*h)
'
fit_skim_log <- sem(model_skim_TBS_log, data = db2)
summary(fit_skim_log,fit.measures=TRUE, standardized=TRUE, ci=TRUE)## lavaan 0.6-18 ended normally after 44 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 24
##
## Used Total
## Number of observations 362 445
##
## Model Test User Model:
##
## Test statistic 120.811
## Degrees of freedom 31
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 155.833
## Degrees of freedom 50
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.151
## Tucker-Lewis Index (TLI) -0.369
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -1717.652
## Loglikelihood unrestricted model (H1) NA
##
## Akaike (AIC) 3483.305
## Bayesian (BIC) 3576.704
## Sample-size adjusted Bayesian (SABIC) 3500.563
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.089
## 90 Percent confidence interval - lower 0.073
## 90 Percent confidence interval - upper 0.107
## P-value H_0: RMSEA <= 0.050 0.000
## P-value H_0: RMSEA >= 0.080 0.834
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.066
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## TBSL1L2L3L4_final ~
## skim (i) -0.047 0.019 -2.488 0.013 -0.083 -0.010
## age_final -0.000 0.001 -0.410 0.682 -0.003 0.002
## female_b2 -0.017 0.019 -0.850 0.396 -0.055 0.022
## PA_SCORE_2 0.000 0.001 0.022 0.982 -0.002 0.003
## vitd_top -0.000 0.001 -0.329 0.742 -0.003 0.002
## BMI_b2 -0.002 0.001 -1.467 0.142 -0.004 0.001
## alchl_fr_8 0.006 0.015 0.420 0.675 -0.023 0.036
## log_IL6 ~
## skim (a) 0.028 0.137 0.203 0.839 -0.240 0.295
## diabts_bn2 0.062 0.118 0.523 0.601 -0.170 0.294
## log_tnf ~
## skim (c) 0.039 0.062 0.638 0.524 -0.082 0.161
## diabts_bn2 0.167 0.054 3.105 0.002 0.061 0.272
## log_il1B ~
## skim (e) -0.031 0.111 -0.283 0.777 -0.248 0.185
## diabts_bn2 -0.145 0.096 -1.512 0.131 -0.333 0.043
## log_crp ~
## skim (g) -0.239 0.161 -1.481 0.139 -0.555 0.077
## diabts_bn2 0.182 0.140 1.305 0.192 -0.092 0.456
## TBSL1L2L3L4_final ~
## log_IL6 (b) 0.010 0.007 1.355 0.175 -0.004 0.024
## log_tnf (d) -0.013 0.016 -0.824 0.410 -0.044 0.018
## log_il1B (f) 0.006 0.009 0.657 0.511 -0.012 0.023
## log_crp (h) -0.013 0.006 -2.206 0.027 -0.025 -0.001
## Std.lv Std.all
##
## -0.047 -0.129
## -0.000 -0.022
## -0.017 -0.045
## 0.000 0.001
## -0.000 -0.017
## -0.002 -0.080
## 0.006 0.022
##
## 0.028 0.011
## 0.062 0.028
##
## 0.039 0.033
## 0.167 0.162
##
## -0.031 -0.015
## -0.145 -0.080
##
## -0.239 -0.078
## 0.182 0.069
##
## 0.010 0.070
## -0.013 -0.042
## 0.006 0.034
## -0.013 -0.113
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## .TBSL1L2L3L4_fn 0.023 0.002 13.454 0.000 0.019 0.026
## .log_IL6 1.210 0.090 13.454 0.000 1.033 1.386
## .log_tnf 0.249 0.018 13.454 0.000 0.212 0.285
## .log_il1B 0.793 0.059 13.454 0.000 0.678 0.909
## .log_crp 1.685 0.125 13.454 0.000 1.440 1.931
## Std.lv Std.all
## 0.023 0.952
## 1.210 0.999
## 0.249 0.971
## 0.793 0.993
## 1.685 0.990
##
## Defined Parameters:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## ab 0.000 0.001 0.201 0.841 -0.002 0.003
## cd -0.001 0.001 -0.504 0.614 -0.002 0.001
## ef -0.000 0.001 -0.260 0.795 -0.002 0.001
## total -0.044 0.019 -2.324 0.020 -0.081 -0.007
## Std.lv Std.all
## 0.000 0.001
## -0.001 -0.001
## -0.000 -0.001
## -0.044 -0.121semPaths(fit_skim_log)
Full fat as predictor, TBS as response, and log transformed mediators
model_fat_TBS <- ' # direct effect
TBSL1L2L3L4_final ~ i*fat
# mediator
log_IL6 ~ a*fat
log_tnf ~ c*fat
log_il1B ~ e*fat
log_crp ~ g*fat
TBSL1L2L3L4_final ~ b*log_IL6
TBSL1L2L3L4_final ~ d*log_tnf
TBSL1L2L3L4_final ~ f*log_il1B
TBSL1L2L3L4_final ~ h*log_crp
# indirect effect (a*b)
ab := a*b
cd := c*d
ef := e*f
# total effect
total := i + (a*b) +(c*d) +(e*f) +(g*h)
'
fit_fat <- sem(model_fat_TBS, data = db2)
summary(fit_fat)## lavaan 0.6-18 ended normally after 31 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 14
##
## Used Total
## Number of observations 396 445
##
## Model Test User Model:
##
## Test statistic 53.030
## Degrees of freedom 6
## P-value (Chi-square) 0.000
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Regressions:
## Estimate Std.Err z-value P(>|z|)
## TBSL1L2L3L4_final ~
## fat (i) 0.014 0.008 1.706 0.088
## log_IL6 ~
## fat (a) -0.123 0.061 -2.032 0.042
## log_tnf ~
## fat (c) -0.013 0.028 -0.458 0.647
## log_il1B ~
## fat (e) -0.017 0.049 -0.356 0.722
## log_crp ~
## fat (g) -0.054 0.071 -0.760 0.447
## TBSL1L2L3L4_final ~
## log_IL6 (b) 0.006 0.007 0.911 0.362
## log_tnf (d) -0.013 0.015 -0.860 0.390
## log_il1B (f) 0.009 0.009 1.038 0.299
## log_crp (h) -0.014 0.006 -2.392 0.017
##
## Variances:
## Estimate Std.Err z-value P(>|z|)
## .TBSL1L2L3L4_fn 0.023 0.002 14.071 0.000
## .log_IL6 1.197 0.085 14.071 0.000
## .log_tnf 0.250 0.018 14.071 0.000
## .log_il1B 0.780 0.055 14.071 0.000
## .log_crp 1.639 0.116 14.071 0.000
##
## Defined Parameters:
## Estimate Std.Err z-value P(>|z|)
## ab -0.001 0.001 -0.831 0.406
## cd 0.000 0.000 0.404 0.686
## ef -0.000 0.000 -0.337 0.736
## total 0.014 0.008 1.698 0.089semPaths(fit2)
#adjusted
model_fat_adj_TBS_log <- ' # direct effect
TBSL1L2L3L4_final ~ i*fat + age_final + female_b2 + PA_SCORE_b2 + vitd_top + BMI_b2 + alcohol_freq_8yr
# mediator
log_IL6 ~ a*fat + diabetes_bone2
log_tnf ~ c*fat + diabetes_bone2
log_il1B ~ e*fat + diabetes_bone2
log_crp ~ g*fat + diabetes_bone2
TBSL1L2L3L4_final ~ b*log_IL6
TBSL1L2L3L4_final ~ d*log_tnf
TBSL1L2L3L4_final ~ f*log_il1B
TBSL1L2L3L4_final ~ h*log_crp
# indirect effect (a*b)
ab := a*b
cd := c*d
ef := e*f
# total effect
total := i + (a*b) +(c*d) +(e*f) +(g*h)
'
fit_fat_log <- sem(model_fat_adj_TBS_log, data = db2)
summary(fit_fat_log,fit.measures=TRUE, standardized=TRUE, ci=TRUE)## lavaan 0.6-18 ended normally after 2 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 24
##
## Used Total
## Number of observations 362 445
##
## Model Test User Model:
##
## Test statistic 122.450
## Degrees of freedom 31
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 158.033
## Degrees of freedom 50
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.153
## Tucker-Lewis Index (TLI) -0.365
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -1717.372
## Loglikelihood unrestricted model (H1) NA
##
## Akaike (AIC) 3482.744
## Bayesian (BIC) 3576.144
## Sample-size adjusted Bayesian (SABIC) 3500.003
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.090
## 90 Percent confidence interval - lower 0.074
## 90 Percent confidence interval - upper 0.107
## P-value H_0: RMSEA <= 0.050 0.000
## P-value H_0: RMSEA >= 0.080 0.853
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.066
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## TBSL1L2L3L4_final ~
## fat (i) 0.021 0.009 2.271 0.023 0.003 0.039
## age_final -0.001 0.001 -0.667 0.505 -0.003 0.002
## female_b2 -0.022 0.019 -1.110 0.267 -0.060 0.017
## PA_SCORE_2 0.000 0.001 0.054 0.957 -0.002 0.003
## vitd_top -0.002 0.001 -1.082 0.279 -0.004 0.001
## BMI_b2 -0.002 0.001 -1.537 0.124 -0.004 0.001
## alchl_fr_8 0.014 0.015 0.932 0.351 -0.016 0.045
## log_IL6 ~
## fat (a) -0.119 0.063 -1.895 0.058 -0.242 0.004
## diabts_bn2 0.057 0.117 0.490 0.624 -0.172 0.287
## log_tnf ~
## fat (c) -0.012 0.029 -0.412 0.680 -0.068 0.044
## diabts_bn2 0.170 0.053 3.188 0.001 0.066 0.275
## log_il1B ~
## fat (e) -0.022 0.051 -0.429 0.668 -0.122 0.078
## diabts_bn2 -0.150 0.095 -1.571 0.116 -0.336 0.037
## log_crp ~
## fat (g) -0.046 0.075 -0.618 0.537 -0.192 0.100
## diabts_bn2 0.155 0.139 1.112 0.266 -0.118 0.428
## TBSL1L2L3L4_final ~
## log_IL6 (b) 0.011 0.007 1.530 0.126 -0.003 0.025
## log_tnf (d) -0.013 0.016 -0.857 0.392 -0.044 0.017
## log_il1B (f) 0.007 0.009 0.765 0.444 -0.011 0.024
## log_crp (h) -0.013 0.006 -2.079 0.038 -0.025 -0.001
## Std.lv Std.all
##
## 0.021 0.126
## -0.001 -0.036
## -0.022 -0.059
## 0.000 0.003
## -0.002 -0.059
## -0.002 -0.083
## 0.014 0.049
##
## -0.119 -0.099
## 0.057 0.026
##
## -0.012 -0.021
## 0.170 0.165
##
## -0.022 -0.022
## -0.150 -0.082
##
## -0.046 -0.032
## 0.155 0.058
##
## 0.011 0.079
## -0.013 -0.044
## 0.007 0.039
## -0.013 -0.107
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## .TBSL1L2L3L4_fn 0.023 0.002 13.454 0.000 0.019 0.026
## .log_IL6 1.198 0.089 13.454 0.000 1.023 1.372
## .log_tnf 0.249 0.018 13.454 0.000 0.213 0.285
## .log_il1B 0.793 0.059 13.454 0.000 0.677 0.908
## .log_crp 1.694 0.126 13.454 0.000 1.447 1.941
## Std.lv Std.all
## 0.023 0.953
## 1.198 0.989
## 0.249 0.972
## 0.793 0.993
## 1.694 0.995
##
## Defined Parameters:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## ab -0.001 0.001 -1.191 0.234 -0.003 0.001
## cd 0.000 0.000 0.371 0.710 -0.001 0.001
## ef -0.000 0.000 -0.374 0.708 -0.001 0.001
## total 0.020 0.009 2.184 0.029 0.002 0.039
## Std.lv Std.all
## -0.001 -0.008
## 0.000 0.001
## -0.000 -0.001
## 0.020 0.122semPaths(fit_fat_log)
####Run adjusted models with “estimator = MLM” since 1 of the independent vars (skim) and all mediator vars aren’t normally distributed
model_milk_mlm <- ' # direct effect
BMSi ~ i*milk
# mediator
IL6 ~ a*milk
TNFa ~ c*milk
IL1B ~ e*milk
CRP ~ g*milk
BMSi ~ b*IL6
BMSi ~ d*TNFa
BMSi ~ f*IL1B
BMSi ~ h*CRP
# indirect effect (a*b)
ab := a*b
cd := c*d
ef := e*f
gh := g*h
# total effect
total := i + (a*b) +(c*d) +(e*f) +(g*h)
'
fit_milk_adj_mlm <- sem(model_milk_mlm, data = db, estimator = "MLM")
summary(fit_milk_adj_mlm, fit.measures=TRUE, standardized=TRUE, ci=TRUE)## lavaan 0.6-18 ended normally after 1 iteration
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 14
##
## Used Total
## Number of observations 151 163
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 8.559 8.020
## Degrees of freedom 6 6
## P-value (Chi-square) 0.200 0.237
## Scaling correction factor 1.067
## Satorra-Bentler correction
##
## Model Test Baseline Model:
##
## Test statistic 21.256 22.634
## Degrees of freedom 15 15
## P-value 0.129 0.092
## Scaling correction factor 0.939
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.591 0.735
## Tucker-Lewis Index (TLI) -0.023 0.338
##
## Robust Comparative Fit Index (CFI) 0.699
## Robust Tucker-Lewis Index (TLI) 0.248
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -2694.485 -2694.485
## Loglikelihood unrestricted model (H1) -2690.206 -2690.206
##
## Akaike (AIC) 5416.970 5416.970
## Bayesian (BIC) 5459.212 5459.212
## Sample-size adjusted Bayesian (SABIC) 5414.904 5414.904
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.053 0.047
## 90 Percent confidence interval - lower 0.000 0.000
## 90 Percent confidence interval - upper 0.127 0.120
## P-value H_0: RMSEA <= 0.050 0.405 0.453
## P-value H_0: RMSEA >= 0.080 0.331 0.282
##
## Robust RMSEA 0.049
## 90 Percent confidence interval - lower 0.000
## 90 Percent confidence interval - upper 0.127
## P-value H_0: Robust RMSEA <= 0.050 0.437
## P-value H_0: Robust RMSEA >= 0.080 0.313
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.050 0.050
##
## Parameter Estimates:
##
## Standard errors Robust.sem
## Information Expected
## Information saturated (h1) model Structured
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## BMSi ~
## milk (i) 0.958 0.768 1.248 0.212 -0.547 2.462
## IL6 ~
## milk (a) -0.588 0.262 -2.241 0.025 -1.102 -0.074
## TNFa ~
## milk (c) 0.682 0.818 0.834 0.404 -0.921 2.286
## IL1B ~
## milk (e) -1.824 2.956 -0.617 0.537 -7.618 3.970
## CRP ~
## milk (g) -1.618 0.600 -2.698 0.007 -2.793 -0.442
## BMSi ~
## IL6 (b) -0.120 0.120 -1.007 0.314 -0.355 0.114
## TNFa (d) -0.029 0.073 -0.398 0.691 -0.171 0.113
## IL1B (f) -0.019 0.027 -0.689 0.491 -0.071 0.034
## CRP (h) -0.079 0.086 -0.922 0.357 -0.248 0.089
## Std.lv Std.all
##
## 0.958 0.093
##
## -0.588 -0.100
##
## 0.682 0.075
##
## -1.824 -0.053
##
## -1.618 -0.196
##
## -0.120 -0.068
## -0.029 -0.026
## -0.019 -0.062
## -0.079 -0.063
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## .BMSi 64.811 7.625 8.500 0.000 49.866 79.756
## .IL6 21.222 13.536 1.568 0.117 -5.307 47.751
## .TNFa 52.186 17.860 2.922 0.003 17.181 87.190
## .IL1B 738.733 144.950 5.096 0.000 454.637 1022.829
## .CRP 40.972 11.123 3.683 0.000 19.171 62.774
## Std.lv Std.all
## 64.811 0.974
## 21.222 0.990
## 52.186 0.994
## 738.733 0.997
## 40.972 0.962
##
## Defined Parameters:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## ab 0.071 0.073 0.972 0.331 -0.072 0.213
## cd -0.020 0.049 -0.399 0.690 -0.117 0.077
## ef 0.034 0.059 0.576 0.565 -0.081 0.149
## gh 0.128 0.153 0.838 0.402 -0.172 0.428
## total 1.171 0.747 1.567 0.117 -0.294 2.636
## Std.lv Std.all
## 0.071 0.007
## -0.020 -0.002
## 0.034 0.003
## 0.128 0.012
## 1.171 0.114semPaths(fit_milk_adj_mlm)
fluid adjusted MLM
model_fluid_mlm <- ' # direct effect
BMSi ~ i*fluid + age_final + female_b2 + PA_SCORE_b2 + vitd_top + BMI_b2 + alcohol_freq_8yr
# mediator
IL6 ~ a*fluid + diabetes_bone2
TNFa ~ c*fluid + diabetes_bone2
IL1B ~ e*fluid + diabetes_bone2
CRP ~ g*fluid + diabetes_bone2
BMSi ~ b*IL6
BMSi ~ d*TNFa
BMSi ~ f*IL1B
BMSi ~ h*CRP
# indirect effect (a*b)
ab := a*b
cd := c*d
ef := e*f
gh := g*h
# total effect
total := i + (a*b) +(c*d) +(e*f) +(g*h)
'
fit_fluid_adj_mlm <- sem(model_fluid_mlm, data = db, estimator = "MLM")
summary(fit_fluid_adj_mlm, fit.measures=TRUE, standardized=TRUE, ci=TRUE)## lavaan 0.6-18 ended normally after 1 iteration
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 24
##
## Used Total
## Number of observations 135 163
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 58.940 53.094
## Degrees of freedom 31 31
## P-value (Chi-square) 0.002 0.008
## Scaling correction factor 1.110
## Satorra-Bentler correction
##
## Model Test Baseline Model:
##
## Test statistic 85.243 84.143
## Degrees of freedom 50 50
## P-value 0.001 0.002
## Scaling correction factor 1.013
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.207 0.353
## Tucker-Lewis Index (TLI) -0.279 -0.044
##
## Robust Comparative Fit Index (CFI) 0.291
## Robust Tucker-Lewis Index (TLI) -0.144
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -2418.397 -2418.397
## Loglikelihood unrestricted model (H1) -2388.927 -2388.927
##
## Akaike (AIC) 4884.794 4884.794
## Bayesian (BIC) 4954.521 4954.521
## Sample-size adjusted Bayesian (SABIC) 4878.601 4878.601
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.082 0.073
## 90 Percent confidence interval - lower 0.049 0.039
## 90 Percent confidence interval - upper 0.113 0.104
## P-value H_0: RMSEA <= 0.050 0.055 0.119
## P-value H_0: RMSEA >= 0.080 0.562 0.373
##
## Robust RMSEA 0.077
## 90 Percent confidence interval - lower 0.039
## 90 Percent confidence interval - upper 0.111
## P-value H_0: Robust RMSEA <= 0.050 0.108
## P-value H_0: Robust RMSEA >= 0.080 0.463
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.067 0.067
##
## Parameter Estimates:
##
## Standard errors Robust.sem
## Information Expected
## Information saturated (h1) model Structured
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## BMSi ~
## fluid (i) 1.733 0.783 2.215 0.027 0.199 3.267
## age_final -0.196 0.106 -1.852 0.064 -0.404 0.011
## female_b2 -0.154 1.871 -0.083 0.934 -3.822 3.514
## PA_SCORE_2 0.170 0.116 1.468 0.142 -0.057 0.397
## vitd_top -0.075 0.129 -0.578 0.564 -0.327 0.178
## BMI_b2 -0.278 0.124 -2.244 0.025 -0.521 -0.035
## alchl_fr_8 -0.135 1.466 -0.092 0.926 -3.009 2.739
## IL6 ~
## fluid (a) -0.546 0.287 -1.904 0.057 -1.108 0.016
## diabts_bn2 -0.443 0.818 -0.541 0.588 -2.045 1.160
## TNFa ~
## fluid (c) 0.777 0.830 0.936 0.349 -0.849 2.403
## diabts_bn2 1.591 1.281 1.242 0.214 -0.920 4.102
## IL1B ~
## fluid (e) -1.519 2.818 -0.539 0.590 -7.041 4.004
## diabts_bn2 -5.714 4.680 -1.221 0.222 -14.885 3.458
## CRP ~
## fluid (g) -1.424 0.494 -2.881 0.004 -2.393 -0.455
## diabts_bn2 1.110 0.992 1.120 0.263 -0.833 3.053
## BMSi ~
## IL6 (b) -0.166 0.106 -1.570 0.116 -0.373 0.041
## TNFa (d) -0.057 0.061 -0.944 0.345 -0.177 0.062
## IL1B (f) -0.028 0.029 -0.959 0.338 -0.084 0.029
## CRP (h) -0.004 0.086 -0.041 0.967 -0.171 0.164
## Std.lv Std.all
##
## 1.733 0.179
## -0.196 -0.157
## -0.154 -0.008
## 0.170 0.122
## -0.075 -0.051
## -0.278 -0.191
## -0.135 -0.009
##
## -0.546 -0.096
## -0.443 -0.045
##
## 0.777 0.089
## 1.591 0.107
##
## -1.519 -0.047
## -5.714 -0.102
##
## -1.424 -0.183
## 1.110 0.083
##
## -0.166 -0.098
## -0.057 -0.052
## -0.028 -0.093
## -0.004 -0.003
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## .BMSi 60.485 7.626 7.931 0.000 45.538 75.433
## .IL6 23.428 14.825 1.580 0.114 -5.629 52.486
## .TNFa 54.173 20.270 2.673 0.008 14.445 93.901
## .IL1B 766.246 161.047 4.758 0.000 450.600 1081.892
## .CRP 42.465 11.570 3.670 0.000 19.789 65.141
## Std.lv Std.all
## 60.485 0.889
## 23.428 0.989
## 54.173 0.982
## 766.246 0.988
## 42.465 0.958
##
## Defined Parameters:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## ab 0.090 0.062 1.465 0.143 -0.031 0.212
## cd -0.045 0.055 -0.813 0.416 -0.152 0.063
## ef 0.042 0.073 0.571 0.568 -0.102 0.185
## gh 0.005 0.122 0.041 0.967 -0.234 0.244
## total 1.826 0.771 2.369 0.018 0.316 3.337
## Std.lv Std.all
## 0.090 0.009
## -0.045 -0.005
## 0.042 0.004
## 0.005 0.001
## 1.826 0.189semPaths(fit_fluid_adj_mlm)
total adjusted MLM
model_total_mlm <- ' # direct effect
BMSi ~ i*mod + age_final + female_b2 + PA_SCORE_b2 + vitd_top + BMI_b2 + alcohol_freq_8yr
# mediator
IL6 ~ a*mod + diabetes_bone2
TNFa ~ c*mod + diabetes_bone2
IL1B ~ e*mod + diabetes_bone2
CRP ~ g*mod + diabetes_bone2
BMSi ~ b*IL6
BMSi ~ d*TNFa
BMSi ~ f*IL1B
BMSi ~ h*CRP
# indirect effect (a*b)
ab := a*b
cd := c*d
ef := e*f
gh := g*h
# total effect
total := i + (a*b) +(c*d) +(e*f) +(g*h)
'
fit_total_adj_mlm <- sem(model_total_mlm, data = db, estimator="MLM")
summary(fit_total_adj_mlm,fit.measures=TRUE, standardized=TRUE,ci=TRUE)## lavaan 0.6-18 ended normally after 1 iteration
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 24
##
## Used Total
## Number of observations 135 163
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 57.896 52.391
## Degrees of freedom 31 31
## P-value (Chi-square) 0.002 0.010
## Scaling correction factor 1.105
## Satorra-Bentler correction
##
## Model Test Baseline Model:
##
## Test statistic 84.737 83.749
## Degrees of freedom 50 50
## P-value 0.002 0.002
## Scaling correction factor 1.012
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.226 0.366
## Tucker-Lewis Index (TLI) -0.249 -0.022
##
## Robust Comparative Fit Index (CFI) 0.308
## Robust Tucker-Lewis Index (TLI) -0.117
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -2418.128 -2418.128
## Loglikelihood unrestricted model (H1) -2389.180 -2389.180
##
## Akaike (AIC) 4884.256 4884.256
## Bayesian (BIC) 4953.983 4953.983
## Sample-size adjusted Bayesian (SABIC) 4878.062 4878.062
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.080 0.071
## 90 Percent confidence interval - lower 0.047 0.037
## 90 Percent confidence interval - upper 0.112 0.103
## P-value H_0: RMSEA <= 0.050 0.064 0.132
## P-value H_0: RMSEA >= 0.080 0.530 0.351
##
## Robust RMSEA 0.075
## 90 Percent confidence interval - lower 0.037
## 90 Percent confidence interval - upper 0.110
## P-value H_0: Robust RMSEA <= 0.050 0.120
## P-value H_0: Robust RMSEA >= 0.080 0.437
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.066 0.066
##
## Parameter Estimates:
##
## Standard errors Robust.sem
## Information Expected
## Information saturated (h1) model Structured
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## BMSi ~
## mod (i) 1.817 0.776 2.342 0.019 0.296 3.337
## age_final -0.189 0.104 -1.819 0.069 -0.394 0.015
## female_b2 -0.232 1.888 -0.123 0.902 -3.932 3.469
## PA_SCORE_2 0.162 0.117 1.381 0.167 -0.068 0.391
## vitd_top -0.087 0.131 -0.665 0.506 -0.344 0.169
## BMI_b2 -0.270 0.124 -2.181 0.029 -0.512 -0.027
## alchl_fr_8 -0.082 1.499 -0.055 0.956 -3.020 2.856
## IL6 ~
## mod (a) -0.473 0.300 -1.579 0.114 -1.061 0.114
## diabts_bn2 -0.441 0.825 -0.534 0.593 -2.058 1.177
## TNFa ~
## mod (c) 0.535 0.841 0.636 0.525 -1.113 2.183
## diabts_bn2 1.576 1.299 1.213 0.225 -0.970 4.121
## IL1B ~
## mod (e) -1.622 2.851 -0.569 0.569 -7.210 3.965
## diabts_bn2 -5.738 4.679 -1.226 0.220 -14.908 3.433
## CRP ~
## mod (g) -1.599 0.501 -3.190 0.001 -2.582 -0.617
## diabts_bn2 1.080 0.986 1.096 0.273 -0.852 3.012
## BMSi ~
## IL6 (b) -0.171 0.111 -1.544 0.123 -0.387 0.046
## TNFa (d) -0.052 0.062 -0.833 0.405 -0.173 0.070
## IL1B (f) -0.027 0.029 -0.929 0.353 -0.083 0.030
## CRP (h) -0.002 0.085 -0.021 0.984 -0.169 0.166
## Std.lv Std.all
##
## 1.817 0.187
## -0.189 -0.151
## -0.232 -0.012
## 0.162 0.116
## -0.087 -0.060
## -0.270 -0.185
## -0.082 -0.005
##
## -0.473 -0.082
## -0.441 -0.045
##
## 0.535 0.061
## 1.576 0.106
##
## -1.622 -0.049
## -5.738 -0.103
##
## -1.599 -0.203
## 1.080 0.081
##
## -0.171 -0.101
## -0.052 -0.047
## -0.027 -0.090
## -0.002 -0.001
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## .BMSi 60.362 7.525 8.021 0.000 45.613 75.111
## .IL6 23.485 14.841 1.582 0.114 -5.604 52.574
## .TNFa 54.407 20.368 2.671 0.008 14.487 94.327
## .IL1B 766.040 160.722 4.766 0.000 451.031 1081.048
## .CRP 42.110 11.469 3.672 0.000 19.632 64.588
## Std.lv Std.all
## 60.362 0.887
## 23.485 0.992
## 54.407 0.986
## 766.040 0.988
## 42.110 0.950
##
## Defined Parameters:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## ab 0.081 0.052 1.561 0.118 -0.021 0.182
## cd -0.028 0.047 -0.588 0.557 -0.120 0.065
## ef 0.043 0.072 0.603 0.547 -0.098 0.185
## gh 0.003 0.137 0.021 0.984 -0.265 0.271
## total 1.916 0.775 2.474 0.013 0.398 3.434
## Std.lv Std.all
## 0.081 0.008
## -0.028 -0.003
## 0.043 0.004
## 0.003 0.000
## 1.916 0.197semPaths(fit_total_adj_mlm)
skim adj MLM
model_skim_TBS_mlm <- ' # direct effect
TBSL1L2L3L4_final ~ i*skim + age_final + female_b2 + PA_SCORE_b2 + vitd_top + BMI_b2 + alcohol_freq_8yr
# mediator
IL6 ~ a*skim + diabetes_bone2
TNFa ~ c*skim + diabetes_bone2
IL1B ~ e*skim + diabetes_bone2
CRP ~ g*skim + diabetes_bone2
TBSL1L2L3L4_final ~ b*IL6
TBSL1L2L3L4_final ~ d*TNFa
TBSL1L2L3L4_final ~ f*IL1B
TBSL1L2L3L4_final ~ h*CRP
# indirect effect (a*b)
ab := a*b
cd := c*d
ef := e*f
gh :=g*h
# total effect
total := i + (a*b) +(c*d) +(e*f) +(g*h)
'
fit_skim_adj_mlm <- sem(model_skim_TBS_mlm, data = db2, estimator="MLM")## Warning: lavaan->lav_data_full():
## some observed variances are (at least) a factor 1000 times larger than
## others; use varTable(fit) to investigatesummary(fit_skim_adj_mlm,fit.measures=TRUE, standardized=TRUE,ci=TRUE)## lavaan 0.6-18 ended normally after 1 iteration
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 24
##
## Used Total
## Number of observations 362 445
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 105.593 71.423
## Degrees of freedom 31 31
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.478
## Satorra-Bentler correction
##
## Model Test Baseline Model:
##
## Test statistic 133.730 106.042
## Degrees of freedom 50 50
## P-value 0.000 0.000
## Scaling correction factor 1.261
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.109 0.279
## Tucker-Lewis Index (TLI) -0.437 -0.163
##
## Robust Comparative Fit Index (CFI) 0.154
## Robust Tucker-Lewis Index (TLI) -0.364
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -5446.680 -5446.680
## Loglikelihood unrestricted model (H1) NA NA
##
## Akaike (AIC) 10941.359 10941.359
## Bayesian (BIC) 11034.759 11034.759
## Sample-size adjusted Bayesian (SABIC) 10958.618 10958.618
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.082 0.060
## 90 Percent confidence interval - lower 0.065 0.045
## 90 Percent confidence interval - upper 0.099 0.075
## P-value H_0: RMSEA <= 0.050 0.001 0.130
## P-value H_0: RMSEA >= 0.080 0.578 0.014
##
## Robust RMSEA 0.073
## 90 Percent confidence interval - lower 0.051
## 90 Percent confidence interval - upper 0.095
## P-value H_0: Robust RMSEA <= 0.050 0.045
## P-value H_0: Robust RMSEA >= 0.080 0.320
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.058 0.058
##
## Parameter Estimates:
##
## Standard errors Robust.sem
## Information Expected
## Information saturated (h1) model Structured
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## TBSL1L2L3L4_final ~
## skim (i) -0.045 0.026 -1.725 0.085 -0.097 0.006
## age_final -0.001 0.001 -0.476 0.634 -0.003 0.002
## female_b2 -0.017 0.019 -0.921 0.357 -0.054 0.019
## PA_SCORE_2 0.000 0.001 0.168 0.867 -0.002 0.002
## vitd_top -0.000 0.001 -0.289 0.772 -0.003 0.002
## BMI_b2 -0.002 0.001 -1.695 0.090 -0.005 0.000
## alchl_fr_8 0.003 0.014 0.237 0.812 -0.024 0.031
## IL6 ~
## skim (a) 0.529 0.860 0.615 0.539 -1.156 2.213
## diabts_bn2 0.789 0.578 1.365 0.172 -0.344 1.922
## TNFa ~
## skim (c) 0.116 0.659 0.175 0.861 -1.175 1.406
## diabts_bn2 1.541 0.786 1.962 0.050 0.002 3.081
## IL1B ~
## skim (e) 2.011 4.313 0.466 0.641 -6.443 10.464
## diabts_bn2 -6.216 4.112 -1.512 0.131 -14.275 1.843
## CRP ~
## skim (g) -2.216 0.937 -2.364 0.018 -4.053 -0.379
## diabts_bn2 2.382 1.106 2.153 0.031 0.214 4.551
## TBSL1L2L3L4_final ~
## IL6 (b) 0.000 0.001 0.315 0.752 -0.002 0.003
## TNFa (d) -0.001 0.001 -0.646 0.518 -0.002 0.001
## IL1B (f) 0.000 0.000 1.563 0.118 -0.000 0.001
## CRP (h) -0.000 0.001 -0.288 0.773 -0.001 0.001
## Std.lv Std.all
##
## -0.045 -0.125
## -0.001 -0.024
## -0.017 -0.047
## 0.000 0.007
## -0.000 -0.016
## -0.002 -0.104
## 0.003 0.011
##
## 0.529 0.038
## 0.789 0.065
##
## 0.116 0.007
## 1.541 0.102
##
## 2.011 0.023
## -6.216 -0.082
##
## -2.216 -0.082
## 2.382 0.102
##
## 0.000 0.015
## -0.001 -0.029
## 0.000 0.058
## -0.000 -0.011
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## .TBSL1L2L3L4_fn 0.023 0.003 8.252 0.000 0.017 0.028
## .IL6 35.848 9.605 3.732 0.000 17.022 54.674
## .TNFa 54.779 16.514 3.317 0.001 22.412 87.146
## .IL1B 1381.734 285.525 4.839 0.000 822.115 1941.353
## .CRP 129.789 54.993 2.360 0.018 22.005 237.573
## Std.lv Std.all
## 0.023 0.963
## 35.848 0.994
## 54.779 0.989
## 1381.734 0.993
## 129.789 0.985
##
## Defined Parameters:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## ab 0.000 0.001 0.299 0.765 -0.001 0.002
## cd -0.000 0.000 -0.164 0.870 -0.001 0.001
## ef 0.000 0.001 0.441 0.659 -0.002 0.003
## gh 0.000 0.001 0.296 0.767 -0.002 0.003
## total -0.044 0.026 -1.707 0.088 -0.095 0.007
## Std.lv Std.all
## 0.000 0.001
## -0.000 -0.000
## 0.000 0.001
## 0.000 0.001
## -0.044 -0.123semPaths(fit_skim_adj_mlm)