RL Regressions_II
2026-08-07
Setup
## [1] 72## [1] 34## [1] 30## [1] 19## [1] 13## [1] 9## [1] 7## [1] 4## [1] 6Results
All values are z-scored
Final Major mean + std
Tier 1 Drop mean + std
Final Major mean * std
Tier 1 Drop mean * std
Final Major mean * std B/W
Tier 1 Drop mean * std B/W
## Takeaway from the GLMs
It seems that the main signal is coming from alpha minus and tier_1_drop_to_zero.
GLMs
Outcome ~ Alpha_minus
alpha_minus_mean_2a1b indirectly proportional to tier_1_drop_to_zero.
##
## Call:
## glm(formula = "tier1_STEM_drop_tozero ~ alpha_minus_mean_2a1b",
## family = binomial, data = jrk_ABG)
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.44403 0.08793 -16.423 <2e-16 ***
## alpha_minus_mean_2a1b -0.23629 0.09671 -2.443 0.0146 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 837.93 on 852 degrees of freedom
## Residual deviance: 831.54 on 851 degrees of freedom
## (22 observations deleted due to missingness)
## AIC: 835.54
##
## Number of Fisher Scoring iterations: 4## Data were 'prettified'. Consider using `terms="alpha_minus_mean_2a1b
## [all]"` to get smooth plots.
##
## Call:
## glm(formula = "final_major_t1_STEM ~ alpha_minus_mean_2a1b",
## family = binomial, data = jrk_ABG)
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.04925 0.06850 0.719 0.472
## alpha_minus_mean_2a1b -0.01440 0.06855 -0.210 0.834
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 1182.0 on 852 degrees of freedom
## Residual deviance: 1181.9 on 851 degrees of freedom
## (22 observations deleted due to missingness)
## AIC: 1185.9
##
## Number of Fisher Scoring iterations: 3## Data were 'prettified'. Consider using `terms="alpha_minus_mean_2a1b
## [all]"` to get smooth plots.
FM ~ alpha minus/plus mean + alpha minus/plus std + beta mean + beta std
alpha_minus_std_2a1b directly proportional to final major
##
## Call:
## glm(formula = "final_major_t1_STEM ~ alpha_minus_mean_2a1b + alpha_minus_std_2a1b + alpha_plus_std_2a1b + alpha_plus_mean_2a1b",
## family = binomial, data = jrk_ABG)
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.09982 0.10027 0.996 0.3195
## alpha_minus_mean_2a1b 0.11122 0.10168 1.094 0.2740
## alpha_minus_std_2a1b 0.22613 0.12547 1.802 0.0715 .
## alpha_plus_std_2a1b -0.04829 0.14417 -0.335 0.7377
## alpha_plus_mean_2a1b 0.09183 0.15719 0.584 0.5591
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 724.43 on 525 degrees of freedom
## Residual deviance: 719.07 on 521 degrees of freedom
## (349 observations deleted due to missingness)
## AIC: 729.07
##
## Number of Fisher Scoring iterations: 4## Data were 'prettified'. Consider using `terms="alpha_minus_mean_2a1b
## [all]"` to get smooth plots.
##
## Call:
## glm(formula = "final_major_t1_STEM ~ alpha_minus_mean_2a1b + alpha_minus_std_2a1b + beta_2a_mean_2a1b + beta_2a1b_std",
## family = binomial, data = jrk_ABG)
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.04902 0.06892 0.711 0.47696
## alpha_minus_mean_2a1b -0.02524 0.10087 -0.250 0.80239
## alpha_minus_std_2a1b 0.26056 0.08693 2.997 0.00272 **
## beta_2a_mean_2a1b 0.02642 0.10209 0.259 0.79579
## beta_2a1b_std -0.12220 0.09055 -1.350 0.17716
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 1182.0 on 852 degrees of freedom
## Residual deviance: 1171.7 on 848 degrees of freedom
## (22 observations deleted due to missingness)
## AIC: 1181.7
##
## Number of Fisher Scoring iterations: 4## Data were 'prettified'. Consider using `terms="alpha_minus_mean_2a1b
## [all]"` to get smooth plots.
##
## Call:
## glm(formula = "final_major_t1_STEM ~ alpha_minus_mean_2a1b + alpha_minus_std_2a1b + alpha_plus_std_2a1b + alpha_plus_mean_2a1b + beta_2a_mean_2a1b + beta_2a1b_std",
## family = binomial, data = jrk_ABG)
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.10017 0.10133 0.989 0.3229
## alpha_minus_mean_2a1b 0.13398 0.16325 0.821 0.4118
## alpha_minus_std_2a1b 0.25991 0.15053 1.727 0.0842 .
## alpha_plus_std_2a1b -0.02356 0.14801 -0.159 0.8735
## alpha_plus_mean_2a1b 0.12252 0.16121 0.760 0.4472
## beta_2a_mean_2a1b -0.13734 0.15302 -0.898 0.3694
## beta_2a1b_std -0.14641 0.12192 -1.201 0.2298
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 724.43 on 525 degrees of freedom
## Residual deviance: 715.86 on 519 degrees of freedom
## (349 observations deleted due to missingness)
## AIC: 729.86
##
## Number of Fisher Scoring iterations: 4## Data were 'prettified'. Consider using `terms="alpha_minus_mean_2a1b
## [all]"` to get smooth plots.
### DTZ ~ alpha minus/plus mean + alpha minus/plus std + beta mean +
beta std
alpha_minus_mean_2a1b and alpha_minus_std_2a1b are both indirectly proportional to DTZ when beta is in the model, but not when alpha_plus is
##
## Call:
## glm(formula = "tier1_STEM_drop_tozero ~ alpha_minus_mean_2a1b + alpha_minus_std_2a1b + alpha_plus_std_2a1b + alpha_plus_mean_2a1b",
## family = binomial, data = jrk_ABG)
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.56782 0.13116 -11.954 <2e-16 ***
## alpha_minus_mean_2a1b -0.28409 0.14519 -1.957 0.0504 .
## alpha_minus_std_2a1b -0.08122 0.16640 -0.488 0.6255
## alpha_plus_std_2a1b 0.18151 0.21199 0.856 0.3919
## alpha_plus_mean_2a1b 0.11600 0.22052 0.526 0.5989
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 475.06 on 525 degrees of freedom
## Residual deviance: 470.00 on 521 degrees of freedom
## (349 observations deleted due to missingness)
## AIC: 480
##
## Number of Fisher Scoring iterations: 4## Data were 'prettified'. Consider using `terms="alpha_minus_mean_2a1b
## [all]"` to get smooth plots.
##
## Call:
## glm(formula = "tier1_STEM_drop_tozero ~ alpha_minus_mean_2a1b + alpha_minus_std_2a1b + beta_2a_mean_2a1b + beta_2a1b_std",
## family = binomial, data = jrk_ABG)
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.45394 0.08856 -16.418 <2e-16 ***
## alpha_minus_mean_2a1b -0.24031 0.11791 -2.038 0.0415 *
## alpha_minus_std_2a1b -0.21281 0.10491 -2.029 0.0425 *
## beta_2a_mean_2a1b -0.05904 0.12087 -0.488 0.6252
## beta_2a1b_std -0.04274 0.10849 -0.394 0.6936
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 837.93 on 852 degrees of freedom
## Residual deviance: 825.40 on 848 degrees of freedom
## (22 observations deleted due to missingness)
## AIC: 835.4
##
## Number of Fisher Scoring iterations: 4## Data were 'prettified'. Consider using `terms="alpha_minus_mean_2a1b
## [all]"` to get smooth plots.
##
## Call:
## glm(formula = "tier1_STEM_drop_tozero ~ alpha_minus_mean_2a1b + alpha_minus_std_2a1b + alpha_plus_std_2a1b + alpha_plus_mean_2a1b + beta_2a_mean_2a1b + beta_2a1b_std",
## family = binomial, data = jrk_ABG)
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.55814 0.13165 -11.836 <2e-16 ***
## alpha_minus_mean_2a1b -0.21041 0.18937 -1.111 0.267
## alpha_minus_std_2a1b -0.15143 0.20244 -0.748 0.454
## alpha_plus_std_2a1b 0.17239 0.21722 0.794 0.427
## alpha_plus_mean_2a1b 0.14628 0.24493 0.597 0.550
## beta_2a_mean_2a1b -0.09219 0.18083 -0.510 0.610
## beta_2a1b_std 0.06898 0.15430 0.447 0.655
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 475.06 on 525 degrees of freedom
## Residual deviance: 469.61 on 519 degrees of freedom
## (349 observations deleted due to missingness)
## AIC: 483.61
##
## Number of Fisher Scoring iterations: 4## Data were 'prettified'. Consider using `terms="alpha_minus_mean_2a1b
## [all]"` to get smooth plots.
FM ~ alpha minus mean * alpha plus mean + semester study
##
## Call:
## glm(formula = "final_major_t1_STEM ~ alpha_plus_mean_2a1b * alpha_minus_mean_2a1b + semester_study + UM_credits_at_study",
## family = binomial, data = jrk_ABG)
##
## Coefficients:
## Estimate Std. Error z value
## (Intercept) 0.971162 0.183348 5.297
## alpha_plus_mean_2a1b 0.085771 0.108074 0.794
## alpha_minus_mean_2a1b 0.105763 0.101373 1.043
## semester_study -0.478161 0.352205 -1.358
## UM_credits_at_study 0.002324 0.022886 0.102
## alpha_plus_mean_2a1b:alpha_minus_mean_2a1b 0.134139 0.115508 1.161
## Pr(>|z|)
## (Intercept) 1.18e-07 ***
## alpha_plus_mean_2a1b 0.427
## alpha_minus_mean_2a1b 0.297
## semester_study 0.175
## UM_credits_at_study 0.919
## alpha_plus_mean_2a1b:alpha_minus_mean_2a1b 0.246
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 724.43 on 525 degrees of freedom
## Residual deviance: 695.46 on 520 degrees of freedom
## (349 observations deleted due to missingness)
## AIC: 707.46
##
## Number of Fisher Scoring iterations: 4## Data were 'prettified'. Consider using `terms="alpha_minus_mean_2a1b
## [all]"` to get smooth plots.
##
## Call:
## glm(formula = "final_major_t1_STEM ~ alpha_plus_mean_2a0b * alpha_minus_mean_2a0b + semester_study + UM_credits_at_study",
## family = binomial, data = jrk_ABG)
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.94291 0.18294 5.154 2.55e-07
## alpha_plus_mean_2a0b -0.02541 0.09843 -0.258 0.796
## alpha_minus_mean_2a0b 0.10737 0.11522 0.932 0.351
## semester_study -0.47497 0.35367 -1.343 0.179
## UM_credits_at_study 0.00184 0.02299 0.080 0.936
## alpha_plus_mean_2a0b:alpha_minus_mean_2a0b -0.10681 0.08900 -1.200 0.230
##
## (Intercept) ***
## alpha_plus_mean_2a0b
## alpha_minus_mean_2a0b
## semester_study
## UM_credits_at_study
## alpha_plus_mean_2a0b:alpha_minus_mean_2a0b
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 724.43 on 525 degrees of freedom
## Residual deviance: 695.63 on 520 degrees of freedom
## (349 observations deleted due to missingness)
## AIC: 707.63
##
## Number of Fisher Scoring iterations: 4## Data were 'prettified'. Consider using `terms="alpha_minus_mean_2a0b
## [all]"` to get smooth plots.
DTZ ~ alpha minus mean * alpha plus mean + semester study
Alpha minus is indirectly proportional to dropout but semester study is directly proportional.
That’s a weird finding, it means the later they participate the likelier they are to drop… Interesting.
This seems to be begging for a survival model, may do a survival model towards the end of this markdown
##
## Call:
## glm(formula = "tier1_STEM_drop_tozero ~ alpha_plus_mean_2a1b * alpha_minus_mean_2a1b + semester_study + UM_credits_at_study",
## family = binomial, data = jrk_ABG)
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.40492 0.23003 -6.107 1.01e-09
## alpha_plus_mean_2a1b -0.06856 0.14683 -0.467 0.64055
## alpha_minus_mean_2a1b -0.31947 0.14930 -2.140 0.03237
## semester_study 1.06637 0.40075 2.661 0.00779
## UM_credits_at_study -0.07773 0.02767 -2.809 0.00497
## alpha_plus_mean_2a1b:alpha_minus_mean_2a1b 0.24106 0.26350 0.915 0.36027
##
## (Intercept) ***
## alpha_plus_mean_2a1b
## alpha_minus_mean_2a1b *
## semester_study **
## UM_credits_at_study **
## alpha_plus_mean_2a1b:alpha_minus_mean_2a1b
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 475.06 on 525 degrees of freedom
## Residual deviance: 462.65 on 520 degrees of freedom
## (349 observations deleted due to missingness)
## AIC: 474.65
##
## Number of Fisher Scoring iterations: 5## Data were 'prettified'. Consider using `terms="alpha_minus_mean_2a1b
## [all]"` to get smooth plots.
##
## Call:
## glm(formula = "tier1_STEM_drop_tozero ~ alpha_mean_1a1b + semester_study + UM_credits_at_study",
## family = binomial, data = jrk_ABG)
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.33762 0.17095 -7.825 5.09e-15 ***
## alpha_mean_1a1b -0.21066 0.10806 -1.949 0.051251 .
## semester_study 1.00222 0.27223 3.682 0.000232 ***
## UM_credits_at_study -0.07254 0.01908 -3.802 0.000144 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 850.16 on 874 degrees of freedom
## Residual deviance: 831.54 on 871 degrees of freedom
## AIC: 839.54
##
## Number of Fisher Scoring iterations: 4## Data were 'prettified'. Consider using `terms="alpha_mean_1a1b [all]"`
## to get smooth plots.
FM ~ alpha_minus mean +/* std (base model)
interestingly the SD of alpha_minus seems to be predictive of final major across a few of these models.
Seems to be a consistent finding
##
## Call:
## glm(formula = "final_major_t1_STEM ~ alpha_minus_std_2a1b + alpha_minus_mean_2a1b",
## family = binomial, data = jrk_ABG)
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.04891 0.06884 0.711 0.47737
## alpha_minus_std_2a1b 0.20488 0.07191 2.849 0.00438 **
## alpha_minus_mean_2a1b 0.03437 0.07165 0.480 0.63144
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 1182.0 on 852 degrees of freedom
## Residual deviance: 1173.7 on 850 degrees of freedom
## (22 observations deleted due to missingness)
## AIC: 1179.7
##
## Number of Fisher Scoring iterations: 4## Data were 'prettified'. Consider using `terms="alpha_minus_mean_2a1b
## [all]"` to get smooth plots.
##
## Call:
## glm(formula = "final_major_t1_STEM ~ alpha_minus_std_2a1b * alpha_minus_mean_2a1b",
## family = binomial, data = jrk_ABG)
##
## Coefficients:
## Estimate Std. Error z value
## (Intercept) 0.0434589 0.0697994 0.623
## alpha_minus_std_2a1b 0.2161975 0.0759182 2.848
## alpha_minus_mean_2a1b 0.0001792 0.1012390 0.002
## alpha_minus_std_2a1b:alpha_minus_mean_2a1b -0.0224746 0.0469709 -0.478
## Pr(>|z|)
## (Intercept) 0.5335
## alpha_minus_std_2a1b 0.0044 **
## alpha_minus_mean_2a1b 0.9986
## alpha_minus_std_2a1b:alpha_minus_mean_2a1b 0.6323
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 1182.0 on 852 degrees of freedom
## Residual deviance: 1173.4 on 849 degrees of freedom
## (22 observations deleted due to missingness)
## AIC: 1181.4
##
## Number of Fisher Scoring iterations: 4## Data were 'prettified'. Consider using `terms="alpha_minus_mean_2a1b
## [all]"` to get smooth plots.
DTZ ~ alpha_minus mean +/* std (base model)
This is fascinating, because both are significant to predicting dropout.
##
## Call:
## glm(formula = "tier1_STEM_drop_tozero ~ alpha_minus_std_2a1b + alpha_minus_mean_2a1b",
## family = binomial, data = jrk_ABG)
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.45255 0.08840 -16.431 < 2e-16 ***
## alpha_minus_std_2a1b -0.21028 0.08656 -2.429 0.01513 *
## alpha_minus_mean_2a1b -0.25574 0.09102 -2.810 0.00496 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 837.93 on 852 degrees of freedom
## Residual deviance: 825.84 on 850 degrees of freedom
## (22 observations deleted due to missingness)
## AIC: 831.84
##
## Number of Fisher Scoring iterations: 4## Data were 'prettified'. Consider using `terms="alpha_minus_mean_2a1b
## [all]"` to get smooth plots.
##
## Call:
## glm(formula = "tier1_STEM_drop_tozero ~ alpha_minus_std_2a1b * alpha_minus_mean_2a1b",
## family = binomial, data = jrk_ABG)
##
## Coefficients:
## Estimate Std. Error z value
## (Intercept) -1.455100 0.090124 -16.146
## alpha_minus_std_2a1b -0.207344 0.088711 -2.337
## alpha_minus_mean_2a1b -0.269848 0.131479 -2.052
## alpha_minus_std_2a1b:alpha_minus_mean_2a1b -0.009447 0.063182 -0.150
## Pr(>|z|)
## (Intercept) <2e-16 ***
## alpha_minus_std_2a1b 0.0194 *
## alpha_minus_mean_2a1b 0.0401 *
## alpha_minus_std_2a1b:alpha_minus_mean_2a1b 0.8811
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 837.93 on 852 degrees of freedom
## Residual deviance: 825.82 on 849 degrees of freedom
## (22 observations deleted due to missingness)
## AIC: 833.82
##
## Number of Fisher Scoring iterations: 4## Data were 'prettified'. Consider using `terms="alpha_minus_mean_2a1b
## [all]"` to get smooth plots.
FM ~ alpha_minus mean + std (1a1b)
##
## Call:
## glm(formula = "final_major_t1_STEM ~ alpha_std_1a1b + alpha_mean_1a1b",
## family = binomial, data = jrk_ABG)
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.075856 0.067724 1.120 0.263
## alpha_std_1a1b -0.002825 0.115080 -0.025 0.980
## alpha_mean_1a1b 0.084949 0.118464 0.717 0.473
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 1211.8 on 874 degrees of freedom
## Residual deviance: 1210.2 on 872 degrees of freedom
## AIC: 1216.2
##
## Number of Fisher Scoring iterations: 4## Data were 'prettified'. Consider using `terms="alpha_mean_1a1b [all]"`
## to get smooth plots.
### DTZ ~ alpha_minus mean + std (1a1b)
##
## Call:
## glm(formula = "tier1_STEM_drop_tozero ~ alpha_std_1a1b + alpha_mean_1a1b",
## family = binomial, data = jrk_ABG)
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.47311 0.08791 -16.757 <2e-16 ***
## alpha_std_1a1b 0.32105 0.17578 1.826 0.0678 .
## alpha_mean_1a1b 0.05978 0.18571 0.322 0.7475
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 850.16 on 874 degrees of freedom
## Residual deviance: 842.45 on 872 degrees of freedom
## AIC: 848.45
##
## Number of Fisher Scoring iterations: 4## Data were 'prettified'. Consider using `terms="alpha_mean_1a1b [all]"`
## to get smooth plots.
Extra Visualizations
n_negative updates
## `geom_smooth()` using formula = 'y ~ x'
n_positive updates
## `geom_smooth()` using formula = 'y ~ x'
n_any updates
## Warning: Groups with fewer than two datapoints have been dropped.
## ℹ Set `drop = FALSE` to consider such groups for position adjustment purposes.
## Groups with fewer than two datapoints have been dropped.
## ℹ Set `drop = FALSE` to consider such groups for position adjustment purposes.## `geom_smooth()` using formula = 'y ~ x'
Follow-Up 1: Range Restriction
So it seems that a lot of these a large amount of variance in the higher ends of alpha_minus_mean. SO like we do for the predictions analyses, it may be good to restrict the range.
quantile(jrk_ABG$alpha_minus_mean_2a1b, na.rm = TRUE, probs = c(0, 0.20, 0.25, 0.40, 0.5, 0.6, 0.75, 0.8, 1))## 0% 20% 25% 40% 50% 60%
## -5.31359627 -0.59059656 -0.45741075 -0.12954038 -0.03473533 0.01142524
## 75% 80% 100%
## 0.27383032 0.42705393 9.01566152ggplot(jrk_ABG, aes(x = "", y = abs(alpha_minus_mean_2a1b))) +
geom_violin(fill = "skyblue", color = "black") +
geom_boxplot(width = 0.1, fill = "white", outlier.shape = NA) +
geom_hline(yintercept = 2, color = "black", linetype = "dashed") +
# geom_hline(yintercept = -2, color = "black", linetype = "dashed") +
labs(
x = NULL,
y = "alpha_minus_mean_2a1b",
title = "Violin Plot of |alpha_minus_mean_2a1b| with Boxplot"
) +
theme_minimal()## Warning: Removed 22 rows containing non-finite outside the scale range
## (`stat_ydensity()`).## Warning: Removed 22 rows containing non-finite outside the scale range
## (`stat_boxplot()`).
pct <- mean(abs(jrk_ABG$alpha_minus_mean_2a1b) <= 2, na.rm = TRUE) * 100
paste0(pct, "% of the data falls between -2 and 2")## [1] "95.5451348182884% of the data falls between -2 and 2"Kind of arbitrary but I’m going to pick to restrict the range to -2 <= x <= 2 (remember this is in standard deviations, so this is keeping anything within 2 standard deviations)
jrk_ABG_RR <- jrk_ABG[abs(jrk_ABG$alpha_minus_mean_2a1b) <= 2,]Outcome ~ Alpha_minus
##
## Call:
## glm(formula = "tier1_STEM_drop_tozero ~ alpha_minus_mean_2a1b",
## family = binomial, data = jrk_ABG_RR)
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.42853 0.09008 -15.858 <2e-16 ***
## alpha_minus_mean_2a1b -0.25237 0.12897 -1.957 0.0504 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 810.08 on 814 degrees of freedom
## Residual deviance: 806.20 on 813 degrees of freedom
## (22 observations deleted due to missingness)
## AIC: 810.2
##
## Number of Fisher Scoring iterations: 4## Data were 'prettified'. Consider using `terms="alpha_minus_mean_2a1b
## [all]"` to get smooth plots.
##
## Call:
## glm(formula = "final_major_t1_STEM ~ alpha_minus_mean_2a1b",
## family = binomial, data = jrk_ABG_RR)
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.03663 0.07044 0.520 0.603
## alpha_minus_mean_2a1b 0.06749 0.10099 0.668 0.504
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 1129.6 on 814 degrees of freedom
## Residual deviance: 1129.2 on 813 degrees of freedom
## (22 observations deleted due to missingness)
## AIC: 1133.2
##
## Number of Fisher Scoring iterations: 3## Data were 'prettified'. Consider using `terms="alpha_minus_mean_2a1b
## [all]"` to get smooth plots.
FM ~ alpha minus/plus mean + alpha minus/plus std + beta mean + beta std
##
## Call:
## glm(formula = "final_major_t1_STEM ~ alpha_minus_mean_2a1b + alpha_minus_std_2a1b + alpha_plus_std_2a1b + alpha_plus_mean_2a1b",
## family = binomial, data = jrk_ABG_RR)
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.03939 0.11023 0.357 0.721
## alpha_minus_mean_2a1b 0.06691 0.15556 0.430 0.667
## alpha_minus_std_2a1b 0.34657 0.15134 2.290 0.022 *
## alpha_plus_std_2a1b -0.05376 0.14670 -0.366 0.714
## alpha_plus_mean_2a1b 0.07809 0.15811 0.494 0.621
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 699.70 on 507 degrees of freedom
## Residual deviance: 692.61 on 503 degrees of freedom
## (329 observations deleted due to missingness)
## AIC: 702.61
##
## Number of Fisher Scoring iterations: 4## Data were 'prettified'. Consider using `terms="alpha_minus_mean_2a1b
## [all]"` to get smooth plots.
##
## Call:
## glm(formula = "final_major_t1_STEM ~ alpha_minus_mean_2a1b + alpha_minus_std_2a1b + beta_2a_mean_2a1b + beta_2a1b_std",
## family = binomial, data = jrk_ABG_RR)
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.009755 0.071679 0.136 0.891746
## alpha_minus_mean_2a1b 0.165777 0.138485 1.197 0.231277
## alpha_minus_std_2a1b 0.312410 0.091599 3.411 0.000648 ***
## beta_2a_mean_2a1b -0.125479 0.116968 -1.073 0.283374
## beta_2a1b_std -0.083629 0.093502 -0.894 0.371104
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 1129.6 on 814 degrees of freedom
## Residual deviance: 1112.7 on 810 degrees of freedom
## (22 observations deleted due to missingness)
## AIC: 1122.7
##
## Number of Fisher Scoring iterations: 4## Data were 'prettified'. Consider using `terms="alpha_minus_mean_2a1b
## [all]"` to get smooth plots.
##
## Call:
## glm(formula = "final_major_t1_STEM ~ alpha_minus_mean_2a1b + alpha_minus_std_2a1b + alpha_plus_std_2a1b + alpha_plus_mean_2a1b + beta_2a_mean_2a1b + beta_2a1b_std",
## family = binomial, data = jrk_ABG_RR)
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.03042 0.11079 0.275 0.7837
## alpha_minus_mean_2a1b 0.28107 0.22994 1.222 0.2216
## alpha_minus_std_2a1b 0.32807 0.16668 1.968 0.0490 *
## alpha_plus_std_2a1b -0.05041 0.15492 -0.325 0.7449
## alpha_plus_mean_2a1b 0.16471 0.16933 0.973 0.3307
## beta_2a_mean_2a1b -0.30164 0.17389 -1.735 0.0828 .
## beta_2a1b_std -0.05621 0.12235 -0.459 0.6459
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 699.70 on 507 degrees of freedom
## Residual deviance: 688.35 on 501 degrees of freedom
## (329 observations deleted due to missingness)
## AIC: 702.35
##
## Number of Fisher Scoring iterations: 4## Data were 'prettified'. Consider using `terms="alpha_minus_mean_2a1b
## [all]"` to get smooth plots.
### DTZ ~ alpha minus/plus mean + alpha minus/plus std + beta mean +
beta std
alpha_minus_mean_2a1b and alpha_minus_std_2a1b are both indirectly proportional to DTZ when beta is in the model, but not when alpha_plus is
##
## Call:
## glm(formula = "tier1_STEM_drop_tozero ~ alpha_minus_mean_2a1b + alpha_minus_std_2a1b + alpha_plus_std_2a1b + alpha_plus_mean_2a1b",
## family = binomial, data = jrk_ABG_RR)
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.4496 0.1357 -10.680 <2e-16 ***
## alpha_minus_mean_2a1b -0.2640 0.1986 -1.329 0.184
## alpha_minus_std_2a1b -0.3020 0.1863 -1.621 0.105
## alpha_plus_std_2a1b 0.1906 0.2114 0.901 0.367
## alpha_plus_mean_2a1b 0.1176 0.2205 0.533 0.594
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 468.34 on 507 degrees of freedom
## Residual deviance: 462.83 on 503 degrees of freedom
## (329 observations deleted due to missingness)
## AIC: 472.83
##
## Number of Fisher Scoring iterations: 4## Data were 'prettified'. Consider using `terms="alpha_minus_mean_2a1b
## [all]"` to get smooth plots.
##
## Call:
## glm(formula = "tier1_STEM_drop_tozero ~ alpha_minus_mean_2a1b + alpha_minus_std_2a1b + beta_2a_mean_2a1b + beta_2a1b_std",
## family = binomial, data = jrk_ABG_RR)
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.42253 0.09053 -15.714 <2e-16 ***
## alpha_minus_mean_2a1b -0.32180 0.15824 -2.034 0.042 *
## alpha_minus_std_2a1b -0.23671 0.10410 -2.274 0.023 *
## beta_2a_mean_2a1b 0.02713 0.12944 0.210 0.834
## beta_2a1b_std -0.09438 0.10461 -0.902 0.367
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 810.08 on 814 degrees of freedom
## Residual deviance: 797.13 on 810 degrees of freedom
## (22 observations deleted due to missingness)
## AIC: 807.13
##
## Number of Fisher Scoring iterations: 4## Data were 'prettified'. Consider using `terms="alpha_minus_mean_2a1b
## [all]"` to get smooth plots.
##
## Call:
## glm(formula = "tier1_STEM_drop_tozero ~ alpha_minus_mean_2a1b + alpha_minus_std_2a1b + alpha_plus_std_2a1b + alpha_plus_mean_2a1b + beta_2a_mean_2a1b + beta_2a1b_std",
## family = binomial, data = jrk_ABG_RR)
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.447963 0.135924 -10.653 <2e-16 ***
## alpha_minus_mean_2a1b -0.358743 0.281574 -1.274 0.203
## alpha_minus_std_2a1b -0.281879 0.207384 -1.359 0.174
## alpha_plus_std_2a1b 0.191710 0.210086 0.913 0.361
## alpha_plus_mean_2a1b 0.074501 0.221684 0.336 0.737
## beta_2a_mean_2a1b 0.120897 0.213430 0.566 0.571
## beta_2a1b_std 0.001104 0.155788 0.007 0.994
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 468.34 on 507 degrees of freedom
## Residual deviance: 462.48 on 501 degrees of freedom
## (329 observations deleted due to missingness)
## AIC: 476.48
##
## Number of Fisher Scoring iterations: 4## Data were 'prettified'. Consider using `terms="alpha_minus_mean_2a1b
## [all]"` to get smooth plots.
FM ~ alpha minus mean * alpha plus mean + semester study
##
## Call:
## glm(formula = "final_major_t1_STEM ~ alpha_plus_mean_2a1b * alpha_minus_mean_2a1b + semester_study + UM_credits_at_study",
## family = binomial, data = jrk_ABG_RR)
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 1.01824 0.18722 5.439 5.36e-08
## alpha_plus_mean_2a1b 0.09013 0.10933 0.824 0.4097
## alpha_minus_mean_2a1b 0.10332 0.15975 0.647 0.5178
## semester_study -0.69888 0.40526 -1.725 0.0846
## UM_credits_at_study 0.01496 0.02619 0.571 0.5677
## alpha_plus_mean_2a1b:alpha_minus_mean_2a1b 0.08032 0.18360 0.437 0.6618
##
## (Intercept) ***
## alpha_plus_mean_2a1b
## alpha_minus_mean_2a1b
## semester_study .
## UM_credits_at_study
## alpha_plus_mean_2a1b:alpha_minus_mean_2a1b
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 699.70 on 507 degrees of freedom
## Residual deviance: 668.59 on 502 degrees of freedom
## (329 observations deleted due to missingness)
## AIC: 680.59
##
## Number of Fisher Scoring iterations: 4## Data were 'prettified'. Consider using `terms="alpha_minus_mean_2a1b
## [all]"` to get smooth plots.
##
## Call:
## glm(formula = "final_major_t1_STEM ~ alpha_plus_mean_2a0b * alpha_minus_mean_2a0b + semester_study + UM_credits_at_study",
## family = binomial, data = jrk_ABG_RR)
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 1.01240 0.18743 5.401 6.61e-08
## alpha_plus_mean_2a0b -0.01385 0.10323 -0.134 0.8933
## alpha_minus_mean_2a0b 0.16829 0.16040 1.049 0.2941
## semester_study -0.68128 0.40863 -1.667 0.0955
## UM_credits_at_study 0.01285 0.02641 0.487 0.6266
## alpha_plus_mean_2a0b:alpha_minus_mean_2a0b -0.13141 0.09572 -1.373 0.1698
##
## (Intercept) ***
## alpha_plus_mean_2a0b
## alpha_minus_mean_2a0b
## semester_study .
## UM_credits_at_study
## alpha_plus_mean_2a0b:alpha_minus_mean_2a0b
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 699.70 on 507 degrees of freedom
## Residual deviance: 666.14 on 502 degrees of freedom
## (329 observations deleted due to missingness)
## AIC: 678.14
##
## Number of Fisher Scoring iterations: 4## Data were 'prettified'. Consider using `terms="alpha_minus_mean_2a0b
## [all]"` to get smooth plots.
DTZ ~ alpha minus mean * alpha plus mean + semester study
Alpha minus is no longer significant semester study is directly proportional.
##
## Call:
## glm(formula = "tier1_STEM_drop_tozero ~ alpha_plus_mean_2a1b * alpha_minus_mean_2a1b + semester_study + UM_credits_at_study",
## family = binomial, data = jrk_ABG_RR)
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.32120 0.23201 -5.695 1.24e-08
## alpha_plus_mean_2a1b -0.07712 0.14662 -0.526 0.59891
## alpha_minus_mean_2a1b -0.32484 0.21082 -1.541 0.12336
## semester_study 1.37598 0.44544 3.089 0.00201
## UM_credits_at_study -0.10020 0.03097 -3.235 0.00122
## alpha_plus_mean_2a1b:alpha_minus_mean_2a1b 0.23388 0.27480 0.851 0.39472
##
## (Intercept) ***
## alpha_plus_mean_2a1b
## alpha_minus_mean_2a1b
## semester_study **
## UM_credits_at_study **
## alpha_plus_mean_2a1b:alpha_minus_mean_2a1b
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 468.34 on 507 degrees of freedom
## Residual deviance: 454.74 on 502 degrees of freedom
## (329 observations deleted due to missingness)
## AIC: 466.74
##
## Number of Fisher Scoring iterations: 4## Data were 'prettified'. Consider using `terms="alpha_minus_mean_2a1b
## [all]"` to get smooth plots.
FM ~ alpha_minus mean +/* std (base model)
interestingly the SD of alpha_minus seems to be predictive of final major across a few of these models.
Seems to be a consistent finding
##
## Call:
## glm(formula = "final_major_t1_STEM ~ alpha_minus_std_2a1b + alpha_minus_mean_2a1b",
## family = binomial, data = jrk_ABG_RR)
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.01031 0.07154 0.144 0.885371
## alpha_minus_std_2a1b 0.30123 0.08129 3.706 0.000211 ***
## alpha_minus_mean_2a1b 0.09983 0.10264 0.973 0.330766
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 1129.6 on 814 degrees of freedom
## Residual deviance: 1114.9 on 812 degrees of freedom
## (22 observations deleted due to missingness)
## AIC: 1120.9
##
## Number of Fisher Scoring iterations: 4## Data were 'prettified'. Consider using `terms="alpha_minus_mean_2a1b
## [all]"` to get smooth plots.
##
## Call:
## glm(formula = "final_major_t1_STEM ~ alpha_minus_std_2a1b * alpha_minus_mean_2a1b",
## family = binomial, data = jrk_ABG_RR)
##
## Coefficients:
## Estimate Std. Error z value
## (Intercept) -0.017242 0.073169 -0.236
## alpha_minus_std_2a1b 0.372767 0.090615 4.114
## alpha_minus_mean_2a1b 0.001126 0.114493 0.010
## alpha_minus_std_2a1b:alpha_minus_mean_2a1b -0.214478 0.111153 -1.930
## Pr(>|z|)
## (Intercept) 0.8137
## alpha_minus_std_2a1b 3.89e-05 ***
## alpha_minus_mean_2a1b 0.9922
## alpha_minus_std_2a1b:alpha_minus_mean_2a1b 0.0537 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 1129.6 on 814 degrees of freedom
## Residual deviance: 1111.2 on 811 degrees of freedom
## (22 observations deleted due to missingness)
## AIC: 1119.2
##
## Number of Fisher Scoring iterations: 4## Data were 'prettified'. Consider using `terms="alpha_minus_mean_2a1b
## [all]"` to get smooth plots.
DTZ ~ alpha_minus mean +/* std (base model)
This is fascinating, because both are significant to predicting dropout.
##
## Call:
## glm(formula = "tier1_STEM_drop_tozero ~ alpha_minus_std_2a1b + alpha_minus_mean_2a1b",
## family = binomial, data = jrk_ABG_RR)
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.42242 0.09044 -15.727 < 2e-16 ***
## alpha_minus_std_2a1b -0.27601 0.09397 -2.937 0.00331 **
## alpha_minus_mean_2a1b -0.27362 0.12412 -2.204 0.02749 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 810.08 on 814 degrees of freedom
## Residual deviance: 797.92 on 812 degrees of freedom
## (22 observations deleted due to missingness)
## AIC: 803.92
##
## Number of Fisher Scoring iterations: 4## Data were 'prettified'. Consider using `terms="alpha_minus_mean_2a1b
## [all]"` to get smooth plots.
##
## Call:
## glm(formula = "tier1_STEM_drop_tozero ~ alpha_minus_std_2a1b * alpha_minus_mean_2a1b",
## family = binomial, data = jrk_ABG_RR)
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.43341 0.09282 -15.443 <2e-16
## alpha_minus_std_2a1b -0.25606 0.10033 -2.552 0.0107
## alpha_minus_mean_2a1b -0.31886 0.14776 -2.158 0.0309
## alpha_minus_std_2a1b:alpha_minus_mean_2a1b -0.07275 0.12729 -0.572 0.5677
##
## (Intercept) ***
## alpha_minus_std_2a1b *
## alpha_minus_mean_2a1b *
## alpha_minus_std_2a1b:alpha_minus_mean_2a1b
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 810.08 on 814 degrees of freedom
## Residual deviance: 797.60 on 811 degrees of freedom
## (22 observations deleted due to missingness)
## AIC: 805.6
##
## Number of Fisher Scoring iterations: 4## Data were 'prettified'. Consider using `terms="alpha_minus_mean_2a1b
## [all]"` to get smooth plots.
Surivival Model
Whole Data alpha minus mean
## Call:
## coxph(formula = Surv(time = jrk_ABG$semester_drop, event = jrk_ABG$tier1_STEM_drop_tozero) ~
## alpha_minus_mean_2a1b, data = jrk_ABG)
##
## n= 853, number of events= 165
## (22 observations deleted due to missingness)
##
## coef exp(coef) se(coef) z Pr(>|z|)
## alpha_minus_mean_2a1b -0.21123 0.80959 0.08373 -2.523 0.0116 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## exp(coef) exp(-coef) lower .95 upper .95
## alpha_minus_mean_2a1b 0.8096 1.235 0.6871 0.954
##
## Concordance= 0.564 (se = 0.024 )
## Likelihood ratio test= 6.52 on 1 df, p=0.01
## Wald test = 6.36 on 1 df, p=0.01
## Score (logrank) test = 5.97 on 1 df, p=0.01Whole Data alpha minus std
## Call:
## coxph(formula = Surv(time = jrk_ABG$semester_drop, event = jrk_ABG$tier1_STEM_drop_tozero) ~
## alpha_minus_std_2a1b, data = jrk_ABG)
##
## n= 853, number of events= 165
## (22 observations deleted due to missingness)
##
## coef exp(coef) se(coef) z Pr(>|z|)
## alpha_minus_std_2a1b -0.13830 0.87083 0.07102 -1.947 0.0515 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## exp(coef) exp(-coef) lower .95 upper .95
## alpha_minus_std_2a1b 0.8708 1.148 0.7577 1.001
##
## Concordance= 0.56 (se = 0.023 )
## Likelihood ratio test= 3.54 on 1 df, p=0.06
## Wald test = 3.79 on 1 df, p=0.05
## Score (logrank) test = 3.81 on 1 df, p=0.05Whole Data alpha minus mean x std
## Call:
## coxph(formula = Surv(time = jrk_ABG$semester_drop, event = jrk_ABG$tier1_STEM_drop_tozero) ~
## alpha_minus_mean_2a1b * alpha_minus_std_2a1b, data = jrk_ABG)
##
## n= 853, number of events= 165
## (22 observations deleted due to missingness)
##
## coef exp(coef) se(coef) z
## alpha_minus_mean_2a1b -0.25326 0.77626 0.11663 -2.172
## alpha_minus_std_2a1b -0.17044 0.84329 0.07507 -2.270
## alpha_minus_mean_2a1b:alpha_minus_std_2a1b -0.02554 0.97478 0.05089 -0.502
## Pr(>|z|)
## alpha_minus_mean_2a1b 0.0299 *
## alpha_minus_std_2a1b 0.0232 *
## alpha_minus_mean_2a1b:alpha_minus_std_2a1b 0.6157
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## exp(coef) exp(-coef) lower .95
## alpha_minus_mean_2a1b 0.7763 1.288 0.6176
## alpha_minus_std_2a1b 0.8433 1.186 0.7279
## alpha_minus_mean_2a1b:alpha_minus_std_2a1b 0.9748 1.026 0.8822
## upper .95
## alpha_minus_mean_2a1b 0.9756
## alpha_minus_std_2a1b 0.9770
## alpha_minus_mean_2a1b:alpha_minus_std_2a1b 1.0770
##
## Concordance= 0.589 (se = 0.023 )
## Likelihood ratio test= 11.89 on 3 df, p=0.008
## Wald test = 13.12 on 3 df, p=0.004
## Score (logrank) test = 13.1 on 3 df, p=0.004
Range Restricted alpha minus mean
## Call:
## coxph(formula = Surv(time = jrk_ABG_RR$semester_drop, event = jrk_ABG_RR$tier1_STEM_drop_tozero) ~
## alpha_minus_mean_2a1b, data = jrk_ABG_RR)
##
## n= 815, number of events= 161
## (22 observations deleted due to missingness)
##
## coef exp(coef) se(coef) z Pr(>|z|)
## alpha_minus_mean_2a1b -0.2385 0.7878 0.1161 -2.055 0.0399 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## exp(coef) exp(-coef) lower .95 upper .95
## alpha_minus_mean_2a1b 0.7878 1.269 0.6275 0.9891
##
## Concordance= 0.558 (se = 0.025 )
## Likelihood ratio test= 4.25 on 1 df, p=0.04
## Wald test = 4.22 on 1 df, p=0.04
## Score (logrank) test = 4.21 on 1 df, p=0.04Range Restricted alpha minus std
## Call:
## coxph(formula = Surv(time = jrk_ABG_RR$semester_drop, event = jrk_ABG_RR$tier1_STEM_drop_tozero) ~
## alpha_minus_std_2a1b, data = jrk_ABG_RR)
##
## n= 815, number of events= 161
## (22 observations deleted due to missingness)
##
## coef exp(coef) se(coef) z Pr(>|z|)
## alpha_minus_std_2a1b -0.21539 0.80623 0.07777 -2.769 0.00561 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## exp(coef) exp(-coef) lower .95 upper .95
## alpha_minus_std_2a1b 0.8062 1.24 0.6922 0.939
##
## Concordance= 0.572 (se = 0.024 )
## Likelihood ratio test= 7 on 1 df, p=0.008
## Wald test = 7.67 on 1 df, p=0.006
## Score (logrank) test = 7.73 on 1 df, p=0.005Range Restricted alpha minus mean x std
## Call:
## coxph(formula = Surv(time = jrk_ABG_RR$semester_drop, event = jrk_ABG_RR$tier1_STEM_drop_tozero) ~
## alpha_minus_mean_2a1b * alpha_minus_std_2a1b, data = jrk_ABG_RR)
##
## n= 815, number of events= 161
## (22 observations deleted due to missingness)
##
## coef exp(coef) se(coef) z
## alpha_minus_mean_2a1b -0.29886 0.74166 0.13279 -2.251
## alpha_minus_std_2a1b -0.21991 0.80259 0.08747 -2.514
## alpha_minus_mean_2a1b:alpha_minus_std_2a1b -0.07527 0.92750 0.11142 -0.675
## Pr(>|z|)
## alpha_minus_mean_2a1b 0.0244 *
## alpha_minus_std_2a1b 0.0119 *
## alpha_minus_mean_2a1b:alpha_minus_std_2a1b 0.4994
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## exp(coef) exp(-coef) lower .95
## alpha_minus_mean_2a1b 0.7417 1.348 0.5717
## alpha_minus_std_2a1b 0.8026 1.246 0.6762
## alpha_minus_mean_2a1b:alpha_minus_std_2a1b 0.9275 1.078 0.7455
## upper .95
## alpha_minus_mean_2a1b 0.9621
## alpha_minus_std_2a1b 0.9527
## alpha_minus_mean_2a1b:alpha_minus_std_2a1b 1.1539
##
## Concordance= 0.588 (se = 0.023 )
## Likelihood ratio test= 12.66 on 3 df, p=0.005
## Wald test = 12.91 on 3 df, p=0.005
## Score (logrank) test = 13.08 on 3 df, p=0.004
