Fit stats: 4 time point (filtered to have one obs. each year), 3 and 4 class solutions
d <- read_csv("ds.csv")## Parsed with column specification:
## cols(
## x6c_16_1 = col_double(),
## x6c_6_2 = col_double(),
## x7c_12_2 = col_double(),
## x7c_8_3 = col_double(),
## x8b_6_2 = col_double(),
## flag = col_double()
## )m3 <- read_rds("m3.rds")
m4 <- read_rds("m4.rds")1 Three Class Solution Output anad Plot
m3## Conditional item response (column) probabilities,
## by outcome variable, for each class (row)
##
## $x6c_6_2
## Pr(1) Pr(2) Pr(3) Pr(4)
## class 1: 0.2358 0.4437 0.1458 0.1747
## class 2: 0.3341 0.4539 0.1524 0.0595
## class 3: 0.3267 0.3028 0.1412 0.2292
##
## $x6c_16_1
## Pr(1) Pr(2) Pr(3) Pr(4)
## class 1: 0.0719 0.5651 0.1620 0.2009
## class 2: 0.2822 0.3992 0.1778 0.1408
## class 3: 0.5822 0.0000 0.0000 0.4178
##
## $x7c_8_3
## Pr(1) Pr(2) Pr(3) Pr(4)
## class 1: 0.0000 0.4903 0.0936 0.4161
## class 2: 0.3899 0.5450 0.0651 0.0000
## class 3: 0.4180 0.0000 0.2122 0.3698
##
## $x7c_12_2
## Pr(1) Pr(2) Pr(3) Pr(4)
## class 1: 0.0000 0.4743 0.0578 0.4679
## class 2: 0.8117 0.0920 0.0000 0.0963
## class 3: 0.4449 0.0458 0.0488 0.4604
##
## Estimated class population shares
## 0.4186 0.348 0.2334
##
## Predicted class memberships (by modal posterior prob.)
## 0.4429 0.3014 0.2557
##
## =========================================================
## Fit for 3 latent classes:
## =========================================================
## number of observations: 219
## number of fully observed cases: 85
## number of estimated parameters: 38
## residual degrees of freedom: 181
## maximum log-likelihood: -867.7372
##
## AIC(3): 1811.474
## BIC(3): 1940.259
## G^2(3): 161.4266 (Likelihood ratio/deviance statistic)
## X^2(3): 276.4603 (Chi-square goodness of fit)
## broom::tidy(m3) %>%
mutate(class_name = rep(str_c(1:3, " (n = ", as.vector(table(m3$predclass)), ")"), 16)) %>%
mutate(variable = factor(variable, levels = c("x6c_6_2", "x6c_16_1", "x7c_8_3", "x7c_12_2", "x8b_6_2"))) %>%
#mutate(class_name = rep(c("Lots of change without a clear pattern", "Steady growth", "Already sophisticated and less simple"), 20)) %>%
ggplot(aes(x = variable, y = estimate, color = as.factor(outcome), group = outcome)) +
facet_wrap(~ class_name) +
geom_point() +
geom_line() +
theme_bw() +
ylab("Probability") +
xlab(NULL) +
theme(text = element_text(size = 15)) +
ylim(0, 1) +
scale_color_discrete("") +
theme(axis.text.x=element_text(angle = 90, hjust = 0))
2 Four Class Solution Output and Plot
m4## Conditional item response (column) probabilities,
## by outcome variable, for each class (row)
##
## $x6c_6_2
## Pr(1) Pr(2) Pr(3) Pr(4)
## class 1: 0.3921 0.3530 0.0000 0.2549
## class 2: 0.4483 0.0000 0.1752 0.3766
## class 3: 0.0000 0.6659 0.3341 0.0000
## class 4: 0.4014 0.4350 0.1002 0.0634
##
## $x6c_16_1
## Pr(1) Pr(2) Pr(3) Pr(4)
## class 1: 0.0887 0.6107 0.0435 0.2571
## class 2: 0.3770 0.0000 0.0000 0.6230
## class 3: 0.3358 0.3834 0.2808 0.0000
## class 4: 0.3218 0.3331 0.1573 0.1878
##
## $x7c_8_3
## Pr(1) Pr(2) Pr(3) Pr(4)
## class 1: 0.0000 0.5459 0.1146 0.3394
## class 2: 0.3533 0.0000 0.2342 0.4124
## class 3: 0.2412 0.3517 0.0543 0.3528
## class 4: 0.4120 0.4938 0.0942 0.0000
##
## $x7c_12_2
## Pr(1) Pr(2) Pr(3) Pr(4)
## class 1: 0.0000 0.6563 0.0306 0.3131
## class 2: 0.3286 0.0000 0.0820 0.5893
## class 3: 0.2150 0.1653 0.0522 0.5674
## class 4: 1.0000 0.0000 0.0000 0.0000
##
## Estimated class population shares
## 0.2991 0.1592 0.2657 0.2761
##
## Predicted class memberships (by modal posterior prob.)
## 0.2603 0.1735 0.2511 0.3151
##
## =========================================================
## Fit for 4 latent classes:
## =========================================================
## number of observations: 219
## number of fully observed cases: 85
## number of estimated parameters: 51
## residual degrees of freedom: 168
## maximum log-likelihood: -862.0112
##
## AIC(4): 1826.022
## BIC(4): 1998.865
## G^2(4): 154.1867 (Likelihood ratio/deviance statistic)
## X^2(4): 260.5505 (Chi-square goodness of fit)
## broom::tidy(m4) %>%
mutate(class_name = rep(str_c(1:4, " (n = ", as.vector(table(m4$predclass)), ")"), 16)) %>%
mutate(variable = factor(variable, levels = c("x6c_6_2", "x6c_16_1", "x7c_8_3", "x7c_12_2", "x8b_6_2"))) %>%
#mutate(class_name = rep(c("Lots of change without a clear pattern", "Steady growth", "Already sophisticated and less simple"), 20)) %>%
ggplot(aes(x = variable, y = estimate, color = as.factor(outcome), group = outcome)) +
facet_wrap(~ class_name) +
geom_point() +
geom_line() +
theme_bw() +
ylab("Probability") +
xlab(NULL) +
theme(text = element_text(size = 15)) +
ylim(0, 1) +
scale_color_discrete("") +
theme(axis.text.x=element_text(angle = 90, hjust = 0))
post_probs <- m3$posterior %>% as.data.frame() %>% setNames(paste0("C", 1:3, "_prob"))
df <- bind_cols(d, post_probs)
df$class <- m3$predclass
df3 <- df %>% mutate_if(is.numeric, round, 3)post_probs <- m4$posterior %>% as.data.frame() %>% setNames(paste0("C", 1:4, "_prob"))
df <- bind_cols(d, post_probs)
df$class <- m4$predclass
df4 <- df %>% mutate_if(is.numeric, round, 3)3 Entropy
A number taking a minumum value of 0 (representing complete concentration of probability on one cell) and a maximum value equal to the logarithm of the total number of cells in the fitted cross-classfication table (representing complete dispersion, or equal probability for outcomes across every cell).
poLCA.entropy(m3)## [1] 4.905256poLCA.entropy(m4)## [1] 4.8348344 Mean classification probabilities
4.1 3 class solution
By class
mat <- df3 %>% dplyr::select(C1_prob:C3_prob, class)
mat %>% group_by(class) %>% summarize_all(funs(mean)) %>% dplyr::select(-class) %>% as.matrix() %>% diag()## Warning: funs() is soft deprecated as of dplyr 0.8.0
## please use list() instead
##
## # Before:
## funs(name = f(.)
##
## # After:
## list(name = ~f(.))
## This warning is displayed once per session.## [1] 0.8584536 0.8954091 0.7340893Overall
mat %>% group_by(class) %>% summarize_all(funs(mean)) %>% dplyr::select(-class) %>% as.matrix() %>% diag() %>% mean()## [1] 0.82931734.2 4 class solution
By class
mat <- df4 %>% dplyr::select(C1_prob:C4_prob, class)
mat %>% group_by(class) %>% summarize_all(funs(mean)) %>% dplyr::select(-class) %>% as.matrix() %>% diag()## [1] 0.8789825 0.7264737 0.7325273 0.8079130Overall
mat %>% group_by(class) %>% summarize_all(funs(mean)) %>% dplyr::select(-class) %>% as.matrix() %>% diag() %>% mean()## [1] 0.78647415 Are certain codes more likely across classes?
5.1 3-class solution
codes_in_class(df3, 1)## For code: 1## Df Sum Sq Mean Sq F value Pr(>F)
## as.factor(class) 3 28.66 9.554 56.97 <2e-16 ***
## Residuals 701 117.56 0.168
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 171 observations deleted due to missingness## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = `1` ~ as.factor(class), data = dfa)
##
## $`as.factor(class)`
## diff lwr upr p adj
## 2-1 0.23427210 0.10944017 0.35910403 0.0000098
## 3-1 0.06576006 -0.04557934 0.17709946 0.4254022
## 4-1 0.48135156 0.37678596 0.58591717 0.0000000
## 3-2 -0.16851204 -0.29430840 -0.04271568 0.0033266
## 4-2 0.24707946 0.12723695 0.36692197 0.0000009
## 4-3 0.41559150 0.30987642 0.52130659 0.0000000codes_in_class(df3, 2)## For code: 2## Df Sum Sq Mean Sq F value Pr(>F)
## as.factor(class) 3 29.53 9.843 52.58 <2e-16 ***
## Residuals 701 131.23 0.187
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 171 observations deleted due to missingness## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = `1` ~ as.factor(class), data = dfa)
##
## $`as.factor(class)`
## diff lwr upr p adj
## 2-1 -0.63387978 -0.7657705 -0.50198911 0.0000000
## 3-1 -0.28160705 -0.3992422 -0.16397186 0.0000000
## 4-1 -0.32820293 -0.4386813 -0.21772456 0.0000000
## 3-2 0.35227273 0.2193631 0.48518236 0.0000000
## 4-2 0.30567686 0.1790577 0.43229598 0.0000000
## 4-3 -0.04659587 -0.1582887 0.06509698 0.7053378codes_in_class(df3, 3)## For code: 3## Df Sum Sq Mean Sq F value Pr(>F)
## as.factor(class) 3 1.45 0.4849 5.379 0.00115 **
## Residuals 701 63.19 0.0901
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 171 observations deleted due to missingness## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = `1` ~ as.factor(class), data = dfa)
##
## $`as.factor(class)`
## diff lwr upr p adj
## 2-1 0.07047779 -0.02104435 0.161999937 0.1953301
## 3-1 0.12127422 0.03964429 0.202904141 0.0008164
## 4-1 0.03378910 -0.04287452 0.110452732 0.6679698
## 3-2 0.05079643 -0.04143281 0.143025657 0.4882533
## 4-2 -0.03668869 -0.12455278 0.051175403 0.7047388
## 4-3 -0.08748511 -0.16499150 -0.009978729 0.0196665codes_in_class(df3, 4)## For code: 4## Df Sum Sq Mean Sq F value Pr(>F)
## as.factor(class) 3 22.03 7.345 46.38 <2e-16 ***
## Residuals 701 111.02 0.158
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 171 observations deleted due to missingness## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = `1` ~ as.factor(class), data = dfa)
##
## $`as.factor(class)`
## diff lwr upr p adj
## 2-1 0.32912989 0.20781838 0.45044140 0.0000000
## 3-1 0.09457278 -0.01362671 0.20277226 0.1108171
## 4-1 -0.18693774 -0.28855446 -0.08532102 0.0000156
## 3-2 -0.23455711 -0.35680585 -0.11230837 0.0000058
## 4-2 -0.51606763 -0.63253043 -0.39960483 0.0000000
## 4-3 -0.28151052 -0.38424431 -0.17877674 0.00000005.2 4-class solution
codes_in_class(df4, 1)## For code: 1## Df Sum Sq Mean Sq F value Pr(>F)
## as.factor(class) 3 28.66 9.554 56.97 <2e-16 ***
## Residuals 701 117.56 0.168
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 171 observations deleted due to missingness## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = `1` ~ as.factor(class), data = dfa)
##
## $`as.factor(class)`
## diff lwr upr p adj
## 2-1 0.23427210 0.10944017 0.35910403 0.0000098
## 3-1 0.06576006 -0.04557934 0.17709946 0.4254022
## 4-1 0.48135156 0.37678596 0.58591717 0.0000000
## 3-2 -0.16851204 -0.29430840 -0.04271568 0.0033266
## 4-2 0.24707946 0.12723695 0.36692197 0.0000009
## 4-3 0.41559150 0.30987642 0.52130659 0.0000000codes_in_class(df4, 2)## For code: 2## Df Sum Sq Mean Sq F value Pr(>F)
## as.factor(class) 3 29.53 9.843 52.58 <2e-16 ***
## Residuals 701 131.23 0.187
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 171 observations deleted due to missingness## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = `1` ~ as.factor(class), data = dfa)
##
## $`as.factor(class)`
## diff lwr upr p adj
## 2-1 -0.63387978 -0.7657705 -0.50198911 0.0000000
## 3-1 -0.28160705 -0.3992422 -0.16397186 0.0000000
## 4-1 -0.32820293 -0.4386813 -0.21772456 0.0000000
## 3-2 0.35227273 0.2193631 0.48518236 0.0000000
## 4-2 0.30567686 0.1790577 0.43229598 0.0000000
## 4-3 -0.04659587 -0.1582887 0.06509698 0.7053378codes_in_class(df4, 3)## For code: 3## Df Sum Sq Mean Sq F value Pr(>F)
## as.factor(class) 3 1.45 0.4849 5.379 0.00115 **
## Residuals 701 63.19 0.0901
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 171 observations deleted due to missingness## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = `1` ~ as.factor(class), data = dfa)
##
## $`as.factor(class)`
## diff lwr upr p adj
## 2-1 0.07047779 -0.02104435 0.161999937 0.1953301
## 3-1 0.12127422 0.03964429 0.202904141 0.0008164
## 4-1 0.03378910 -0.04287452 0.110452732 0.6679698
## 3-2 0.05079643 -0.04143281 0.143025657 0.4882533
## 4-2 -0.03668869 -0.12455278 0.051175403 0.7047388
## 4-3 -0.08748511 -0.16499150 -0.009978729 0.0196665codes_in_class(df4, 4)## For code: 4## Df Sum Sq Mean Sq F value Pr(>F)
## as.factor(class) 3 22.03 7.345 46.38 <2e-16 ***
## Residuals 701 111.02 0.158
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 171 observations deleted due to missingness## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = `1` ~ as.factor(class), data = dfa)
##
## $`as.factor(class)`
## diff lwr upr p adj
## 2-1 0.32912989 0.20781838 0.45044140 0.0000000
## 3-1 0.09457278 -0.01362671 0.20277226 0.1108171
## 4-1 -0.18693774 -0.28855446 -0.08532102 0.0000156
## 3-2 -0.23455711 -0.35680585 -0.11230837 0.0000058
## 4-2 -0.51606763 -0.63253043 -0.39960483 0.0000000
## 4-3 -0.28151052 -0.38424431 -0.17877674 0.0000000- Code 1 is more likely in class 4 than class 3, 2, and 1
- Code 1 is more liely in classes 3 and 2 than in class 1, though Code 1 does not differ between classes 3 and 2
6 Are certain codes in one class more likely at a specific timepoint?
6.1 For 3-class solution
codes_at_time(df3, my_code = 1, my_class = 1)## Code is: 1; Class is: 1## Df Sum Sq Mean Sq F value Pr(>F)
## time 3 3.554 1.1846 20.75 1.38e-11 ***
## Residuals 179 10.217 0.0571
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 45 observations deleted due to missingness## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = `1` ~ time, data = dfa_class1)
##
## $time
## diff lwr upr p adj
## x6c_6_2-x6c_16_1 3.319357e-01 0.1854450 0.47842639 0.0000001
## x7c_12_2-x6c_16_1 -7.547170e-02 -0.1964033 0.04545992 0.3708549
## x7c_8_3-x6c_16_1 -7.547170e-02 -0.1970003 0.04605690 0.3753090
## x7c_12_2-x6c_6_2 -4.074074e-01 -0.5543727 -0.26044210 0.0000000
## x7c_8_3-x6c_6_2 -4.074074e-01 -0.5548643 -0.25995049 0.0000000
## x7c_8_3-x7c_12_2 1.804112e-16 -0.1221003 0.12210029 1.0000000codes_at_time(df3, my_code = 2, my_class = 1)## Code is: 2; Class is: 1## Df Sum Sq Mean Sq F value Pr(>F)
## time 3 4.46 1.4877 7.007 0.000176 ***
## Residuals 179 38.01 0.2123
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 45 observations deleted due to missingness## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = `1` ~ time, data = dfa_class1)
##
## $time
## diff lwr upr p adj
## x6c_6_2-x6c_16_1 -0.38294899 -0.66549321 -0.10040476 0.0031028
## x7c_12_2-x6c_16_1 0.10921626 -0.12403087 0.34246338 0.6185921
## x7c_8_3-x6c_16_1 -0.07140215 -0.30580069 0.16299640 0.8589371
## x7c_12_2-x6c_6_2 0.49216524 0.20870559 0.77562490 0.0000708
## x7c_8_3-x6c_6_2 0.31154684 0.02713898 0.59595470 0.0256346
## x7c_8_3-x7c_12_2 -0.18061840 -0.41611960 0.05488279 0.1959932codes_at_time(df3, my_code = 3, my_class = 1)## Code is: 3; Class is: 1## Df Sum Sq Mean Sq F value Pr(>F)
## time 3 0.359 0.1197 2.613 0.0528 .
## Residuals 179 8.198 0.0458
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 45 observations deleted due to missingness## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = `1` ~ time, data = dfa_class1)
##
## $time
## diff lwr upr p adj
## x6c_6_2-x6c_16_1 -0.01886792 -0.15009358 0.1123577 0.9822613
## x7c_12_2-x6c_16_1 0.01959361 -0.08873635 0.1279236 0.9657465
## x7c_8_3-x6c_16_1 0.09877913 -0.01008560 0.2076439 0.0901543
## x7c_12_2-x6c_6_2 0.03846154 -0.09318928 0.1701124 0.8732897
## x7c_8_3-x6c_6_2 0.11764706 -0.01444414 0.2497383 0.0996263
## x7c_8_3-x7c_12_2 0.07918552 -0.03019133 0.1885624 0.2414135codes_at_time(df3, my_code = 4, my_class = 1)## Code is: 4; Class is: 1## Df Sum Sq Mean Sq F value Pr(>F)
## time 3 0.38 0.1281 0.705 0.55
## Residuals 179 32.51 0.1816
## 45 observations deleted due to missingness## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = `1` ~ time, data = dfa_class1)
##
## $time
## diff lwr upr p adj
## x6c_6_2-x6c_16_1 0.06988120 -0.1914413 0.3312037 0.8994773
## x7c_12_2-x6c_16_1 -0.05333817 -0.2690662 0.1623899 0.9184883
## x7c_8_3-x6c_16_1 0.04809471 -0.1686983 0.2648877 0.9393508
## x7c_12_2-x6c_6_2 -0.12321937 -0.3853885 0.1389498 0.6157051
## x7c_8_3-x6c_6_2 -0.02178649 -0.2848326 0.2412596 0.9964882
## x7c_8_3-x7c_12_2 0.10143288 -0.1163799 0.3192457 0.6227862codes_at_time(df3, my_code = 1, my_class = 2)## Code is: 1; Class is: 2## Df Sum Sq Mean Sq F value Pr(>F)
## time 3 0.483 0.1608 0.732 0.535
## Residuals 113 24.817 0.2196
## 35 observations deleted due to missingness## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = `1` ~ time, data = dfa_class1)
##
## $time
## diff lwr upr p adj
## x6c_6_2-x6c_16_1 0.184873950 -0.1763933 0.5461412 0.5430766
## x7c_12_2-x6c_16_1 -0.004464286 -0.3033559 0.2944274 0.9999787
## x7c_8_3-x6c_16_1 0.017316017 -0.2792005 0.3138325 0.9987345
## x7c_12_2-x6c_6_2 -0.189338235 -0.5560999 0.1774235 0.5356716
## x7c_8_3-x6c_6_2 -0.167557932 -0.5323866 0.1972707 0.6295981
## x7c_8_3-x7c_12_2 0.021780303 -0.2814064 0.3249670 0.9976550codes_at_time(df3, my_code = 2, my_class = 2)## Code is: 2; Class is: 2## Df Sum Sq Mean Sq F value Pr(>F)
## time 3 0 0
## Residuals 113 0 0
## 35 observations deleted due to missingness## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = `1` ~ time, data = dfa_class1)
##
## $time
## diff lwr upr p adj
## x6c_6_2-x6c_16_1 0 0 0 NaN
## x7c_12_2-x6c_16_1 0 0 0 NaN
## x7c_8_3-x6c_16_1 0 0 0 NaN
## x7c_12_2-x6c_6_2 0 0 0 NaN
## x7c_8_3-x6c_6_2 0 0 0 NaN
## x7c_8_3-x7c_12_2 0 0 0 NaNcodes_at_time(df3, my_code = 3, my_class = 2)## Code is: 3; Class is: 2## Df Sum Sq Mean Sq F value Pr(>F)
## time 3 1.296 0.4320 4.426 0.00557 **
## Residuals 113 11.029 0.0976
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 35 observations deleted due to missingness## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = `1` ~ time, data = dfa_class1)
##
## $time
## diff lwr upr p adj
## x6c_6_2-x6c_16_1 0.11764706 -0.12319024 0.3584844 0.5814285
## x7c_12_2-x6c_16_1 0.09375000 -0.10550487 0.2930049 0.6111315
## x7c_8_3-x6c_16_1 0.27272727 0.07505579 0.4703988 0.0026565
## x7c_12_2-x6c_6_2 -0.02389706 -0.26839722 0.2206031 0.9941615
## x7c_8_3-x6c_6_2 0.15508021 -0.08813130 0.3982917 0.3482201
## x7c_8_3-x7c_12_2 0.17897727 -0.02314086 0.3810954 0.1020097codes_at_time(df3, my_code = 4, my_class = 2)## Code is: 4; Class is: 2## Df Sum Sq Mean Sq F value Pr(>F)
## time 3 1.948 0.6494 2.736 0.0469 *
## Residuals 113 26.821 0.2374
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 35 observations deleted due to missingness## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = `1` ~ time, data = dfa_class1)
##
## $time
## diff lwr upr p adj
## x6c_6_2-x6c_16_1 -0.30252101 -0.6780953 0.07305325 0.1592288
## x7c_12_2-x6c_16_1 -0.08928571 -0.4000142 0.22144273 0.8767905
## x7c_8_3-x6c_16_1 -0.29004329 -0.5983025 0.01821594 0.0730337
## x7c_12_2-x6c_6_2 0.21323529 -0.1680510 0.59452161 0.4660503
## x7c_8_3-x6c_6_2 0.01247772 -0.3667990 0.39175445 0.9997724
## x7c_8_3-x7c_12_2 -0.20075758 -0.5159511 0.11443599 0.3492034codes_at_time(df3, my_code = 1, my_class = 3)## Code is: 1; Class is: 3## Df Sum Sq Mean Sq F value Pr(>F)
## time 3 2.521 0.8404 7.361 0.000114 ***
## Residuals 172 19.638 0.1142
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 44 observations deleted due to missingness## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = `1` ~ time, data = dfa_class1)
##
## $time
## diff lwr upr p adj
## x6c_6_2-x6c_16_1 -0.31914894 -0.51650951 -0.12178836 0.0002531
## x7c_12_2-x6c_16_1 -0.25792445 -0.43690050 -0.07894839 0.0014251
## x7c_8_3-x6c_16_1 -0.14523589 -0.32704679 0.03657501 0.1663117
## x7c_12_2-x6c_6_2 0.06122449 -0.13443812 0.25688710 0.8488380
## x7c_8_3-x6c_6_2 0.17391304 -0.02434595 0.37217204 0.1077603
## x7c_8_3-x7c_12_2 0.11268855 -0.06727772 0.29265483 0.3676139codes_at_time(df3, my_code = 2, my_class = 3)## Code is: 2; Class is: 3## Df Sum Sq Mean Sq F value Pr(>F)
## time 3 5.76 1.919 9.597 6.82e-06 ***
## Residuals 172 34.40 0.200
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 44 observations deleted due to missingness## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = `1` ~ time, data = dfa_class1)
##
## $time
## diff lwr upr p adj
## x6c_6_2-x6c_16_1 0.31476846 0.05355277 0.57598415 0.0110867
## x7c_12_2-x6c_16_1 -0.21884498 -0.45572792 0.01803795 0.0814988
## x7c_8_3-x6c_16_1 -0.03561517 -0.27625015 0.20501981 0.9806883
## x7c_12_2-x6c_6_2 -0.53361345 -0.79258179 -0.27464510 0.0000017
## x7c_8_3-x6c_6_2 -0.35038363 -0.61278842 -0.08797885 0.0037191
## x7c_8_3-x7c_12_2 0.18322981 -0.05496373 0.42142335 0.1936192codes_at_time(df3, my_code = 3, my_class = 3)## Code is: 3; Class is: 3## Df Sum Sq Mean Sq F value Pr(>F)
## time 3 3.401 1.1337 9.076 1.31e-05 ***
## Residuals 172 21.485 0.1249
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 44 observations deleted due to missingness## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = `1` ~ time, data = dfa_class1)
##
## $time
## diff lwr upr p adj
## x6c_6_2-x6c_16_1 0.004380476 -0.2020555 0.21081645 0.9999399
## x7c_12_2-x6c_16_1 -0.278332610 -0.4655387 -0.09112655 0.0009244
## x7c_8_3-x6c_16_1 -0.275670675 -0.4658419 -0.08549942 0.0013162
## x7c_12_2-x6c_6_2 -0.282713085 -0.4873730 -0.07805317 0.0024678
## x7c_8_3-x6c_6_2 -0.280051151 -0.4874269 -0.07267545 0.0032538
## x7c_8_3-x7c_12_2 0.002661934 -0.1855799 0.19090375 0.9999822codes_at_time(df3, my_code = 4, my_class = 3)## Code is: 4; Class is: 3## Df Sum Sq Mean Sq F value Pr(>F)
## time 3 18.41 6.137 51.56 <2e-16 ***
## Residuals 172 20.47 0.119
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 44 observations deleted due to missingness## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = `1` ~ time, data = dfa_class1)
##
## $time
## diff lwr upr p adj
## x6c_6_2-x6c_16_1 3.436967e-16 -0.2015201 0.2015201 1.0000000
## x7c_12_2-x6c_16_1 7.551020e-01 0.5723540 0.9378501 0.0000000
## x7c_8_3-x6c_16_1 4.565217e-01 0.2708791 0.6421644 0.0000000
## x7c_12_2-x6c_6_2 7.551020e-01 0.5553157 0.9548884 0.0000000
## x7c_8_3-x6c_6_2 4.565217e-01 0.2540843 0.6589592 0.0000001
## x7c_8_3-x7c_12_2 -2.985803e-01 -0.4823395 -0.1148211 0.0002337codes_at_time(df3, my_code = 1, my_class = 4)## Code is: 1; Class is: 4## Df Sum Sq Mean Sq F value Pr(>F)
## time 3 16.42 5.472 30.85 <2e-16 ***
## Residuals 225 39.92 0.177
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 47 observations deleted due to missingness## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = `1` ~ time, data = dfa_class1)
##
## $time
## diff lwr upr p adj
## x6c_6_2-x6c_16_1 0.01713287 -0.1956947 0.2299604 0.9967933
## x7c_12_2-x6c_16_1 0.63076923 0.4372398 0.8242986 0.0000000
## x7c_8_3-x6c_16_1 0.07904509 -0.1178702 0.2759604 0.7267135
## x7c_12_2-x6c_6_2 0.61363636 0.3987403 0.8285324 0.0000000
## x7c_8_3-x6c_6_2 0.06191223 -0.1560380 0.2798625 0.8828050
## x7c_8_3-x7c_12_2 -0.55172414 -0.7508733 -0.3525750 0.0000000codes_at_time(df3, my_code = 2, my_class = 4)## Code is: 2; Class is: 4## Df Sum Sq Mean Sq F value Pr(>F)
## time 3 8.66 2.8856 16.25 1.35e-09 ***
## Residuals 225 39.95 0.1775
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 47 observations deleted due to missingness## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = `1` ~ time, data = dfa_class1)
##
## $time
## diff lwr upr p adj
## x6c_6_2-x6c_16_1 0.11608392 -0.09682518 0.3289930 0.4936405
## x7c_12_2-x6c_16_1 -0.33846154 -0.53206509 -0.1448580 0.0000576
## x7c_8_3-x6c_16_1 0.14429708 -0.05269368 0.3412878 0.2326809
## x7c_12_2-x6c_6_2 -0.45454545 -0.66952381 -0.2395671 0.0000007
## x7c_8_3-x6c_6_2 0.02821317 -0.18982059 0.2462469 0.9870231
## x7c_8_3-x7c_12_2 0.48275862 0.28353320 0.6819840 0.0000000codes_at_time(df3, my_code = 3, my_class = 4)## Code is: 3; Class is: 4## Df Sum Sq Mean Sq F value Pr(>F)
## time 3 0.806 0.26870 3.638 0.0136 *
## Residuals 225 16.617 0.07386
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 47 observations deleted due to missingness## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = `1` ~ time, data = dfa_class1)
##
## $time
## diff lwr upr p adj
## x6c_6_2-x6c_16_1 -0.04020979 -0.17753238 0.09711280 0.8732034
## x7c_12_2-x6c_16_1 -0.15384615 -0.27871701 -0.02897530 0.0087994
## x7c_8_3-x6c_16_1 -0.08488064 -0.21193619 0.04217491 0.3109941
## x7c_12_2-x6c_6_2 -0.11363636 -0.25229359 0.02502086 0.1494847
## x7c_8_3-x6c_6_2 -0.04467085 -0.18529875 0.09595706 0.8439287
## x7c_8_3-x7c_12_2 0.06896552 -0.05953135 0.19746238 0.5074316codes_at_time(df3, my_code = 4, my_class = 4)## Code is: 4; Class is: 4## Df Sum Sq Mean Sq F value Pr(>F)
## time 3 0.809 0.26956 6.277 0.000415 ***
## Residuals 225 9.663 0.04295
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 47 observations deleted due to missingness## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = `1` ~ time, data = dfa_class1)
##
## $time
## diff lwr upr p adj
## x6c_6_2-x6c_16_1 -9.300699e-02 -0.19772317 0.01170919 0.1013262
## x7c_12_2-x6c_16_1 -1.384615e-01 -0.23368257 -0.04324050 0.0012160
## x7c_8_3-x6c_16_1 -1.384615e-01 -0.23534852 -0.04157455 0.0015418
## x7c_12_2-x6c_6_2 -4.545455e-02 -0.15118846 0.06027937 0.6820855
## x7c_8_3-x6c_6_2 -4.545455e-02 -0.15269121 0.06178212 0.6916646
## x7c_8_3-x7c_12_2 -1.804112e-16 -0.09798607 0.09798607 1.00000006.2 For 4-class solution
codes_at_time(df4, my_code = 1, my_class = 1)## Code is: 1; Class is: 1## Df Sum Sq Mean Sq F value Pr(>F)
## time 3 3.554 1.1846 20.75 1.38e-11 ***
## Residuals 179 10.217 0.0571
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 45 observations deleted due to missingness## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = `1` ~ time, data = dfa_class1)
##
## $time
## diff lwr upr p adj
## x6c_6_2-x6c_16_1 3.319357e-01 0.1854450 0.47842639 0.0000001
## x7c_12_2-x6c_16_1 -7.547170e-02 -0.1964033 0.04545992 0.3708549
## x7c_8_3-x6c_16_1 -7.547170e-02 -0.1970003 0.04605690 0.3753090
## x7c_12_2-x6c_6_2 -4.074074e-01 -0.5543727 -0.26044210 0.0000000
## x7c_8_3-x6c_6_2 -4.074074e-01 -0.5548643 -0.25995049 0.0000000
## x7c_8_3-x7c_12_2 1.804112e-16 -0.1221003 0.12210029 1.0000000codes_at_time(df4, my_code = 2, my_class = 1)## Code is: 2; Class is: 1## Df Sum Sq Mean Sq F value Pr(>F)
## time 3 4.46 1.4877 7.007 0.000176 ***
## Residuals 179 38.01 0.2123
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 45 observations deleted due to missingness## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = `1` ~ time, data = dfa_class1)
##
## $time
## diff lwr upr p adj
## x6c_6_2-x6c_16_1 -0.38294899 -0.66549321 -0.10040476 0.0031028
## x7c_12_2-x6c_16_1 0.10921626 -0.12403087 0.34246338 0.6185921
## x7c_8_3-x6c_16_1 -0.07140215 -0.30580069 0.16299640 0.8589371
## x7c_12_2-x6c_6_2 0.49216524 0.20870559 0.77562490 0.0000708
## x7c_8_3-x6c_6_2 0.31154684 0.02713898 0.59595470 0.0256346
## x7c_8_3-x7c_12_2 -0.18061840 -0.41611960 0.05488279 0.1959932codes_at_time(df4, my_code = 3, my_class = 1)## Code is: 3; Class is: 1## Df Sum Sq Mean Sq F value Pr(>F)
## time 3 0.359 0.1197 2.613 0.0528 .
## Residuals 179 8.198 0.0458
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 45 observations deleted due to missingness## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = `1` ~ time, data = dfa_class1)
##
## $time
## diff lwr upr p adj
## x6c_6_2-x6c_16_1 -0.01886792 -0.15009358 0.1123577 0.9822613
## x7c_12_2-x6c_16_1 0.01959361 -0.08873635 0.1279236 0.9657465
## x7c_8_3-x6c_16_1 0.09877913 -0.01008560 0.2076439 0.0901543
## x7c_12_2-x6c_6_2 0.03846154 -0.09318928 0.1701124 0.8732897
## x7c_8_3-x6c_6_2 0.11764706 -0.01444414 0.2497383 0.0996263
## x7c_8_3-x7c_12_2 0.07918552 -0.03019133 0.1885624 0.2414135codes_at_time(df4, my_code = 4, my_class = 1)## Code is: 4; Class is: 1## Df Sum Sq Mean Sq F value Pr(>F)
## time 3 0.38 0.1281 0.705 0.55
## Residuals 179 32.51 0.1816
## 45 observations deleted due to missingness## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = `1` ~ time, data = dfa_class1)
##
## $time
## diff lwr upr p adj
## x6c_6_2-x6c_16_1 0.06988120 -0.1914413 0.3312037 0.8994773
## x7c_12_2-x6c_16_1 -0.05333817 -0.2690662 0.1623899 0.9184883
## x7c_8_3-x6c_16_1 0.04809471 -0.1686983 0.2648877 0.9393508
## x7c_12_2-x6c_6_2 -0.12321937 -0.3853885 0.1389498 0.6157051
## x7c_8_3-x6c_6_2 -0.02178649 -0.2848326 0.2412596 0.9964882
## x7c_8_3-x7c_12_2 0.10143288 -0.1163799 0.3192457 0.6227862codes_at_time(df4, my_code = 1, my_class = 2)## Code is: 1; Class is: 2## Df Sum Sq Mean Sq F value Pr(>F)
## time 3 0.483 0.1608 0.732 0.535
## Residuals 113 24.817 0.2196
## 35 observations deleted due to missingness## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = `1` ~ time, data = dfa_class1)
##
## $time
## diff lwr upr p adj
## x6c_6_2-x6c_16_1 0.184873950 -0.1763933 0.5461412 0.5430766
## x7c_12_2-x6c_16_1 -0.004464286 -0.3033559 0.2944274 0.9999787
## x7c_8_3-x6c_16_1 0.017316017 -0.2792005 0.3138325 0.9987345
## x7c_12_2-x6c_6_2 -0.189338235 -0.5560999 0.1774235 0.5356716
## x7c_8_3-x6c_6_2 -0.167557932 -0.5323866 0.1972707 0.6295981
## x7c_8_3-x7c_12_2 0.021780303 -0.2814064 0.3249670 0.9976550codes_at_time(df4, my_code = 2, my_class = 2)## Code is: 2; Class is: 2## Df Sum Sq Mean Sq F value Pr(>F)
## time 3 0 0
## Residuals 113 0 0
## 35 observations deleted due to missingness## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = `1` ~ time, data = dfa_class1)
##
## $time
## diff lwr upr p adj
## x6c_6_2-x6c_16_1 0 0 0 NaN
## x7c_12_2-x6c_16_1 0 0 0 NaN
## x7c_8_3-x6c_16_1 0 0 0 NaN
## x7c_12_2-x6c_6_2 0 0 0 NaN
## x7c_8_3-x6c_6_2 0 0 0 NaN
## x7c_8_3-x7c_12_2 0 0 0 NaNcodes_at_time(df4, my_code = 3, my_class = 2)## Code is: 3; Class is: 2## Df Sum Sq Mean Sq F value Pr(>F)
## time 3 1.296 0.4320 4.426 0.00557 **
## Residuals 113 11.029 0.0976
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 35 observations deleted due to missingness## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = `1` ~ time, data = dfa_class1)
##
## $time
## diff lwr upr p adj
## x6c_6_2-x6c_16_1 0.11764706 -0.12319024 0.3584844 0.5814285
## x7c_12_2-x6c_16_1 0.09375000 -0.10550487 0.2930049 0.6111315
## x7c_8_3-x6c_16_1 0.27272727 0.07505579 0.4703988 0.0026565
## x7c_12_2-x6c_6_2 -0.02389706 -0.26839722 0.2206031 0.9941615
## x7c_8_3-x6c_6_2 0.15508021 -0.08813130 0.3982917 0.3482201
## x7c_8_3-x7c_12_2 0.17897727 -0.02314086 0.3810954 0.1020097codes_at_time(df4, my_code = 4, my_class = 2)## Code is: 4; Class is: 2## Df Sum Sq Mean Sq F value Pr(>F)
## time 3 1.948 0.6494 2.736 0.0469 *
## Residuals 113 26.821 0.2374
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 35 observations deleted due to missingness## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = `1` ~ time, data = dfa_class1)
##
## $time
## diff lwr upr p adj
## x6c_6_2-x6c_16_1 -0.30252101 -0.6780953 0.07305325 0.1592288
## x7c_12_2-x6c_16_1 -0.08928571 -0.4000142 0.22144273 0.8767905
## x7c_8_3-x6c_16_1 -0.29004329 -0.5983025 0.01821594 0.0730337
## x7c_12_2-x6c_6_2 0.21323529 -0.1680510 0.59452161 0.4660503
## x7c_8_3-x6c_6_2 0.01247772 -0.3667990 0.39175445 0.9997724
## x7c_8_3-x7c_12_2 -0.20075758 -0.5159511 0.11443599 0.3492034codes_at_time(df4, my_code = 1, my_class = 3)## Code is: 1; Class is: 3## Df Sum Sq Mean Sq F value Pr(>F)
## time 3 2.521 0.8404 7.361 0.000114 ***
## Residuals 172 19.638 0.1142
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 44 observations deleted due to missingness## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = `1` ~ time, data = dfa_class1)
##
## $time
## diff lwr upr p adj
## x6c_6_2-x6c_16_1 -0.31914894 -0.51650951 -0.12178836 0.0002531
## x7c_12_2-x6c_16_1 -0.25792445 -0.43690050 -0.07894839 0.0014251
## x7c_8_3-x6c_16_1 -0.14523589 -0.32704679 0.03657501 0.1663117
## x7c_12_2-x6c_6_2 0.06122449 -0.13443812 0.25688710 0.8488380
## x7c_8_3-x6c_6_2 0.17391304 -0.02434595 0.37217204 0.1077603
## x7c_8_3-x7c_12_2 0.11268855 -0.06727772 0.29265483 0.3676139codes_at_time(df4, my_code = 2, my_class = 3)## Code is: 2; Class is: 3## Df Sum Sq Mean Sq F value Pr(>F)
## time 3 5.76 1.919 9.597 6.82e-06 ***
## Residuals 172 34.40 0.200
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 44 observations deleted due to missingness## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = `1` ~ time, data = dfa_class1)
##
## $time
## diff lwr upr p adj
## x6c_6_2-x6c_16_1 0.31476846 0.05355277 0.57598415 0.0110867
## x7c_12_2-x6c_16_1 -0.21884498 -0.45572792 0.01803795 0.0814988
## x7c_8_3-x6c_16_1 -0.03561517 -0.27625015 0.20501981 0.9806883
## x7c_12_2-x6c_6_2 -0.53361345 -0.79258179 -0.27464510 0.0000017
## x7c_8_3-x6c_6_2 -0.35038363 -0.61278842 -0.08797885 0.0037191
## x7c_8_3-x7c_12_2 0.18322981 -0.05496373 0.42142335 0.1936192codes_at_time(df4, my_code = 3, my_class = 3)## Code is: 3; Class is: 3## Df Sum Sq Mean Sq F value Pr(>F)
## time 3 3.401 1.1337 9.076 1.31e-05 ***
## Residuals 172 21.485 0.1249
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 44 observations deleted due to missingness## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = `1` ~ time, data = dfa_class1)
##
## $time
## diff lwr upr p adj
## x6c_6_2-x6c_16_1 0.004380476 -0.2020555 0.21081645 0.9999399
## x7c_12_2-x6c_16_1 -0.278332610 -0.4655387 -0.09112655 0.0009244
## x7c_8_3-x6c_16_1 -0.275670675 -0.4658419 -0.08549942 0.0013162
## x7c_12_2-x6c_6_2 -0.282713085 -0.4873730 -0.07805317 0.0024678
## x7c_8_3-x6c_6_2 -0.280051151 -0.4874269 -0.07267545 0.0032538
## x7c_8_3-x7c_12_2 0.002661934 -0.1855799 0.19090375 0.9999822codes_at_time(df4, my_code = 4, my_class = 3)## Code is: 4; Class is: 3## Df Sum Sq Mean Sq F value Pr(>F)
## time 3 18.41 6.137 51.56 <2e-16 ***
## Residuals 172 20.47 0.119
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 44 observations deleted due to missingness## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = `1` ~ time, data = dfa_class1)
##
## $time
## diff lwr upr p adj
## x6c_6_2-x6c_16_1 3.436967e-16 -0.2015201 0.2015201 1.0000000
## x7c_12_2-x6c_16_1 7.551020e-01 0.5723540 0.9378501 0.0000000
## x7c_8_3-x6c_16_1 4.565217e-01 0.2708791 0.6421644 0.0000000
## x7c_12_2-x6c_6_2 7.551020e-01 0.5553157 0.9548884 0.0000000
## x7c_8_3-x6c_6_2 4.565217e-01 0.2540843 0.6589592 0.0000001
## x7c_8_3-x7c_12_2 -2.985803e-01 -0.4823395 -0.1148211 0.0002337codes_at_time(df4, my_code = 1, my_class = 4)## Code is: 1; Class is: 4## Df Sum Sq Mean Sq F value Pr(>F)
## time 3 16.42 5.472 30.85 <2e-16 ***
## Residuals 225 39.92 0.177
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 47 observations deleted due to missingness## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = `1` ~ time, data = dfa_class1)
##
## $time
## diff lwr upr p adj
## x6c_6_2-x6c_16_1 0.01713287 -0.1956947 0.2299604 0.9967933
## x7c_12_2-x6c_16_1 0.63076923 0.4372398 0.8242986 0.0000000
## x7c_8_3-x6c_16_1 0.07904509 -0.1178702 0.2759604 0.7267135
## x7c_12_2-x6c_6_2 0.61363636 0.3987403 0.8285324 0.0000000
## x7c_8_3-x6c_6_2 0.06191223 -0.1560380 0.2798625 0.8828050
## x7c_8_3-x7c_12_2 -0.55172414 -0.7508733 -0.3525750 0.0000000codes_at_time(df4, my_code = 2, my_class = 4)## Code is: 2; Class is: 4## Df Sum Sq Mean Sq F value Pr(>F)
## time 3 8.66 2.8856 16.25 1.35e-09 ***
## Residuals 225 39.95 0.1775
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 47 observations deleted due to missingness## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = `1` ~ time, data = dfa_class1)
##
## $time
## diff lwr upr p adj
## x6c_6_2-x6c_16_1 0.11608392 -0.09682518 0.3289930 0.4936405
## x7c_12_2-x6c_16_1 -0.33846154 -0.53206509 -0.1448580 0.0000576
## x7c_8_3-x6c_16_1 0.14429708 -0.05269368 0.3412878 0.2326809
## x7c_12_2-x6c_6_2 -0.45454545 -0.66952381 -0.2395671 0.0000007
## x7c_8_3-x6c_6_2 0.02821317 -0.18982059 0.2462469 0.9870231
## x7c_8_3-x7c_12_2 0.48275862 0.28353320 0.6819840 0.0000000codes_at_time(df4, my_code = 3, my_class = 4)## Code is: 3; Class is: 4## Df Sum Sq Mean Sq F value Pr(>F)
## time 3 0.806 0.26870 3.638 0.0136 *
## Residuals 225 16.617 0.07386
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 47 observations deleted due to missingness## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = `1` ~ time, data = dfa_class1)
##
## $time
## diff lwr upr p adj
## x6c_6_2-x6c_16_1 -0.04020979 -0.17753238 0.09711280 0.8732034
## x7c_12_2-x6c_16_1 -0.15384615 -0.27871701 -0.02897530 0.0087994
## x7c_8_3-x6c_16_1 -0.08488064 -0.21193619 0.04217491 0.3109941
## x7c_12_2-x6c_6_2 -0.11363636 -0.25229359 0.02502086 0.1494847
## x7c_8_3-x6c_6_2 -0.04467085 -0.18529875 0.09595706 0.8439287
## x7c_8_3-x7c_12_2 0.06896552 -0.05953135 0.19746238 0.5074316codes_at_time(df4, my_code = 4, my_class = 4)## Code is: 4; Class is: 4## Df Sum Sq Mean Sq F value Pr(>F)
## time 3 0.809 0.26956 6.277 0.000415 ***
## Residuals 225 9.663 0.04295
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 47 observations deleted due to missingness## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = `1` ~ time, data = dfa_class1)
##
## $time
## diff lwr upr p adj
## x6c_6_2-x6c_16_1 -9.300699e-02 -0.19772317 0.01170919 0.1013262
## x7c_12_2-x6c_16_1 -1.384615e-01 -0.23368257 -0.04324050 0.0012160
## x7c_8_3-x6c_16_1 -1.384615e-01 -0.23534852 -0.04157455 0.0015418
## x7c_12_2-x6c_6_2 -4.545455e-02 -0.15118846 0.06027937 0.6820855
## x7c_8_3-x6c_6_2 -4.545455e-02 -0.15269121 0.06178212 0.6916646
## x7c_8_3-x7c_12_2 -1.804112e-16 -0.09798607 0.09798607 1.00000007 Homogeneity and Separation
When latent class c is highly homogeneous, members of are likely to provide the same observed response pattern, implying that one response pattern is characteristic of the class. If homogeneity is low, no single response pattern stands out.
When latent class separation is good, the pattern of item-response probabiltiies across indicator variables clearly differentiates among the latent classes. When there is high separation, a response pattern that enmerges as characteristic of a particular latent class will be characteristic of that class only (and will not be characteristic of any of the other latent classes).
7.1 3 class solution
df3 %>%
dplyr::select(-class) %>%
gather(class, prob, C1_prob, C2_prob, C3_prob) %>%
mutate_if(is.integer, replace_na, 0) %>%
unite(response_pattern, x6c_6_2, x6c_16_1, x7c_8_3, x7c_12_2, sep = "-") %>%
group_by(class, response_pattern) %>%
summarize(mean_post_prob = mean(prob),
n = n()) %>%
ungroup() %>%
spread(class, mean_post_prob) %>%
mutate_if(is.double, round, 3) %>%
arrange(desc(n)) %>%
print(n = 20)## # A tibble: 143 x 5
## response_pattern n C1_prob C2_prob C3_prob
## <chr> <int> <dbl> <dbl> <dbl>
## 1 NA-2-2-2 8 0.888 0.112 0
## 2 NA-2-4-2 5 1 0 0
## 3 NA-2-4-4 5 1 0 0
## 4 NA-4-4-4 5 0.497 0 0.503
## 5 2-2-1-1 4 0 1 0
## 6 2-2-2-4 4 0.879 0.121 0
## 7 NA-2-2-1 4 0 1 0
## 8 2-2-2-1 3 0 1 0
## 9 2-2-2-2 3 0.885 0.115 0
## 10 NA-1-1-1 3 0 0.551 0.449
## 11 NA-1-1-4 3 0 0.124 0.876
## 12 NA-1-2-1 3 0 1 0
## 13 NA-1-4-4 3 0.202 0 0.798
## 14 NA-1-NA-1 3 0 0.569 0.431
## 15 NA-2-2-4 3 0.882 0.118 0
## 16 NA-3-4-4 3 1 0 0
## 17 1-1-1-4 2 0 0.126 0.874
## 18 1-2-4-2 2 1 0 0
## 19 1-4-2-1 2 0 1 0
## 20 1-4-2-2 2 0.849 0.151 0
## # … with 123 more rows7.2 4 class solution
df4 %>%
dplyr::select(-class) %>%
gather(class, prob, C1_prob, C2_prob, C3_prob, C4_prob) %>%
mutate_if(is.integer, replace_na, 0) %>%
unite(response_pattern, x6c_6_2, x6c_16_1, x7c_8_3, x7c_12_2, sep = "-") %>%
mutate(n_NA = str_count(response_pattern, "NA")) %>%
filter(n_NA <= 2) %>%
group_by(class, response_pattern) %>%
summarize(mean_post_prob = mean(prob),
n = n()) %>%
ungroup() %>%
spread(class, mean_post_prob) %>%
mutate_if(is.double, round, 3) %>%
arrange(desc(n)) %>%
print(n = 20)## # A tibble: 143 x 6
## response_pattern n C1_prob C2_prob C3_prob C4_prob
## <chr> <int> <dbl> <dbl> <dbl> <dbl>
## 1 NA-2-2-2 8 0.917 0 0.083 0
## 2 NA-2-4-2 5 0.873 0 0.127 0
## 3 NA-2-4-4 5 0.488 0 0.512 0
## 4 NA-4-4-4 5 0.253 0.747 0 0
## 5 2-2-1-1 4 0 0 0.176 0.824
## 6 2-2-2-4 4 0.449 0 0.551 0
## 7 NA-2-2-1 4 0 0 0.145 0.855
## 8 2-2-2-1 3 0 0 0.206 0.794
## 9 2-2-2-2 3 0.854 0 0.146 0
## 10 NA-1-1-1 3 0 0.145 0.096 0.759
## 11 NA-1-1-4 3 0 0.506 0.494 0
## 12 NA-1-2-1 3 0 0 0.133 0.867
## 13 NA-1-4-4 3 0.08 0.414 0.506 0
## 14 NA-1-NA-1 3 0 0.154 0.15 0.695
## 15 NA-2-2-4 3 0.606 0 0.394 0
## 16 NA-3-4-4 3 0.085 0 0.915 0
## 17 1-1-1-4 2 0 1 0 0
## 18 1-2-4-2 2 1 0 0 0
## 19 1-4-2-1 2 0 0 0 1
## 20 1-4-2-2 2 1 0 0 0
## # … with 123 more rows