# Additional results from the simulations not included in the manuscript

## Table of Contents

## 1 Performance metrics for \(\alpha=.01,.10\)

### 1.1 Between-items designs

- \(\alpha\)=.01

Type I Type I Power Power C.Power C.Power 12 24 12 24 12 24 min-\(F'\) .009 .009 .079 .154 .210 .328 LMEM, Maximal, \(\chi^2_{LR}\) .017 .013 .118 .185 .223 .342 LMEM, Max-NRC, \(\chi^2_{LR}\) .017 .013 .117 .185 .223 .343 \(F_1{\times}F_2\) .014 .019 .106 .222 .224 .337 LMEM, Max-NWI \(\chi^2_{LR}\) .021 .015 .135 .202 .223 .342 LMEM, Maximal, \(t\) .029 .017 .162 .214 .222 .343 LMEM, Max-NRC, \(t\) .029 .017 .162 .214 .223 .343 LMEM, Max-NWI, \(t\) .037 .021 .186 .234 .222 .342 LMEM, RI-only, \(\chi^2_{LR}\) .032 .039 .164 .279 .216 .314 LMEM, RI-only, \(t\) .055 .051 .228 .318 .217 .314 LMEM, RI-only, MCMC .071 .103 .252 .444 .205 .309 \(F_1\) .297 .217 .541 .571 .134 .212

- \(\alpha\)=.10

Type I Type I Power Power C.Power C.Power 12 24 12 24 12 24 min-\(F'\) .092 .093 .311 .444 .210 .328 LMEM, Maximal, \(\chi^2_{LR}\) .129 .113 .371 .478 .223 .342 LMEM, Max-NRC, \(\chi^2_{LR}\) .128 .112 .370 .477 .223 .343 \(F_1{\times}F_2\) .120 .137 .355 .510 .224 .337 LMEM, Max-NWI \(\chi^2_{LR}\) .142 .123 .391 .492 .223 .342 LMEM, Maximal, \(t\) .143 .120 .394 .490 .222 .343 LMEM, Max-NRC, \(t\) .143 .119 .393 .489 .223 .343 LMEM, Max-NWI, \(t\) .160 .131 .415 .505 .222 .342 LMEM, RI-only, \(\chi^2_{LR}\) .171 .177 .419 .548 .216 .314 LMEM, RI-only, \(t\) .193 .189 .447 .563 .217 .314 LMEM, RI-only, MCMC .255 .294 .524 .680 .205 .309 \(F_1\) .497 .420 .732 .767 .134 .212

### 1.2 Within-items designs

- Note: corrected power for the LMEM, RI-only MCMC technique is estimated in the two tables below because the high Type I error rate along with the relatively small number of MCMC runs (10000) provided limited resolution.

- \(\alpha\)=.01

Type I Type I Power Power C.Power C.Power 12 24 12 24 12 24 min-\(F'\) .004 .005 .129 .266 .327 .512 LMEM, Maximal, \(\chi^2_{LR}\) .013 .012 .240 .382 .433 .591 LMEM, Max-NRC, \(\chi^2_{LR}\) .013 .012 .241 .381 .432 .593 \(F_1{\times}F_2\) .012 .018 .212 .410 .416 .578 LMEM, Max-NWI \(\chi^2_{LR}\) .012 .012 .215 .363 .416 .579 LMEM, Maximal, \(t\) .022 .016 .306 .425 .434 .592 LMEM, Max-NRC, \(t\) .023 .016 .308 .425 .432 .593 LMEM, Max-NWI, \(t\) .022 .018 .287 .416 .416 .580 \(F_1\) .083 .059 .455 .538 .345 .506 LMEM, RI-only, \(\chi^2_{LR}\) .317 .377 .787 .904 .379 .531 LMEM, RI-only, \(t\) .320 .379 .789 .904 .379 .531 LMEM, RI-only, MCMC .291 .361 .772 .899 .379 .531

- \(\alpha\)=.10

Type I Type I Power Power C.Power C.Power 12 24 12 24 12 24 min-\(F'\) .061 .068 .463 .643 .327 .512 LMEM, Maximal, \(\chi^2_{LR}\) .113 .108 .582 .717 .433 .591 LMEM, Max-NRC, \(\chi^2_{LR}\) .113 .107 .582 .717 .432 .593 \(F_1{\times}F_2\) .112 .130 .568 .746 .416 .578 LMEM, Max-NWI \(\chi^2_{LR}\) .107 .108 .561 .708 .416 .579 LMEM, Maximal, \(t\) .126 .115 .603 .727 .434 .592 LMEM, Max-NRC, \(t\) .127 .115 .604 .727 .432 .593 LMEM, Max-NWI, \(t\) .121 .115 .586 .722 .416 .58 \(F_1\) .251 .210 .725 .800 .345 .506 LMEM, RI-only, \(\chi^2_{LR}\) .514 .567 .883 .949 .379 .531 LMEM, RI-only, \(t\) .515 .568 .883 .949 .379 .531 LMEM, RI-only, MCMC .491 .554 .876 .947 .379 .531

## 2 Heatmaps for 12-item designs

### 2.1 Between items

- Type I Error

- Power

### 2.2 Within items

- Type I Error

- Power

## 3 Performance of model selection

### 3.1 Between-items design