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1

Lin, Lu, and Runchu Zhang. "Profile quasi-likelihood." Statistics & Probability Letters 56, no. 2 (January 2002): 147–54. http://dx.doi.org/10.1016/s0167-7152(01)00168-7.

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2

Flynn, Cheryl, and Patrick Perry. "Profile likelihood biclustering." Electronic Journal of Statistics 14, no. 1 (2020): 731–68. http://dx.doi.org/10.1214/19-ejs1667.

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3

Murphy, S. A., and A. W. Van Der Vaart. "On Profile Likelihood." Journal of the American Statistical Association 95, no. 450 (June 2000): 449–65. http://dx.doi.org/10.1080/01621459.2000.10474219.

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4

Cole, S. R., H. Chu, and S. Greenland. "Maximum Likelihood, Profile Likelihood, and Penalized Likelihood: A Primer." American Journal of Epidemiology 179, no. 2 (October 29, 2013): 252–60. http://dx.doi.org/10.1093/aje/kwt245.

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5

Bickel, Peter J., and Ya'acov Ritov. "On Profile Likelihood: Comment." Journal of the American Statistical Association 95, no. 450 (June 2000): 466. http://dx.doi.org/10.2307/2669387.

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6

Fan, Jianqing, and Wing-Hung Wong. "On Profile Likelihood: Comment." Journal of the American Statistical Association 95, no. 450 (June 2000): 468. http://dx.doi.org/10.2307/2669388.

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7

Li, Bing. "On Profile Likelihood: Comment." Journal of the American Statistical Association 95, no. 450 (June 2000): 472. http://dx.doi.org/10.2307/2669389.

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8

Shen, Xiaotong. "On Profile Likelihood: Comment." Journal of the American Statistical Association 95, no. 450 (June 2000): 474. http://dx.doi.org/10.2307/2669390.

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9

Robins, James M., Andrea Rotnitzky, and Mark van der Laan. "On Profile Likelihood: Comment." Journal of the American Statistical Association 95, no. 450 (June 2000): 477. http://dx.doi.org/10.2307/2669391.

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10

Murphy, S. A., and A. W. van der Vaart. "On Profile Likelihood: Rejoinder." Journal of the American Statistical Association 95, no. 450 (June 2000): 482. http://dx.doi.org/10.2307/2669392.

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11

Ferrari, Silvia L. P., Fernando Lucambio, and Francisco Cribari-Neto. "Improved profile likelihood inference." Journal of Statistical Planning and Inference 134, no. 2 (October 2005): 373–91. http://dx.doi.org/10.1016/j.jspi.2004.05.001.

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12

FRASER, D. A. S., and N. REID. "Adjustments to profile likelihood." Biometrika 76, no. 3 (1989): 477–88. http://dx.doi.org/10.1093/biomet/76.3.477.

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13

Barndorff-Nielsen, O. E. "Adjusted Versions of Profile Likelihood and Directed Likelihood, and Extended Likelihood." Journal of the Royal Statistical Society: Series B (Methodological) 56, no. 1 (January 1994): 125–40. http://dx.doi.org/10.1111/j.2517-6161.1994.tb01965.x.

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14

Kreutz, Clemens, Andreas Raue, Daniel Kaschek, and Jens Timmer. "Profile likelihood in systems biology." FEBS Journal 280, no. 11 (May 9, 2013): 2564–71. http://dx.doi.org/10.1111/febs.12276.

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15

Zhang, Zhiwei. "Profile Likelihood and Incomplete Data." International Statistical Review 78, no. 1 (April 2010): 102–16. http://dx.doi.org/10.1111/j.1751-5823.2010.00107.x.

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16

Fletcher, David, and Daniel Turek. "Model-Averaged Profile Likelihood Intervals." Journal of Agricultural, Biological, and Environmental Statistics 17, no. 1 (October 5, 2011): 38–51. http://dx.doi.org/10.1007/s13253-011-0064-8.

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17

Dhaene, Geert, and Koen Jochmans. "LIKELIHOOD INFERENCE IN AN AUTOREGRESSION WITH FIXED EFFECTS." Econometric Theory 32, no. 5 (May 11, 2015): 1178–215. http://dx.doi.org/10.1017/s0266466615000146.

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We calculate the bias of the profile score for the regression coefficients in a multistratum autoregressive model with stratum-specific intercepts. The bias is free of incidental parameters. Centering the profile score delivers an unbiased estimating equation and, upon integration, an adjusted profile likelihood. A variety of other approaches to constructing modified profile likelihoods are shown to yield equivalent results. However, the global maximizer of the adjusted likelihood lies at infinity for any sample size, and the adjusted profile score has multiple zeros. Consistent parameter estimates are obtained as local maximizers inside or on an ellipsoid centered at the maximum likelihood estimator.
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18

Ferrari, Silvia L. P., and Francisco Cribari-Neto. "Corrected modified profile likelihood heteroskedasticity tests." Statistics & Probability Letters 57, no. 4 (May 2002): 353–61. http://dx.doi.org/10.1016/s0167-7152(02)00087-1.

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19

Severini, Thomas A., and Wing Hung Wong. "Profile Likelihood and Conditionally Parametric Models." Annals of Statistics 20, no. 4 (December 1992): 1768–802. http://dx.doi.org/10.1214/aos/1176348889.

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20

BARNDORFF-NIELSEN, OLE E., and PETER MCCULLAGH. "A note on the relation between modified profile likelihood and the Cox-Reid adjusted profile likelihood." Biometrika 80, no. 2 (1993): 321–28. http://dx.doi.org/10.1093/biomet/80.2.321.

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21

Simpson, Matthew J., Alexander P. Browning, Christopher Drovandi, Elliot J. Carr, Oliver J. Maclaren, and Ruth E. Baker. "Profile likelihood analysis for a stochastic model of diffusion in heterogeneous media." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 477, no. 2250 (June 2021): 20210214. http://dx.doi.org/10.1098/rspa.2021.0214.

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We compute profile likelihoods for a stochastic model of diffusive transport motivated by experimental observations of heat conduction in layered skin tissues. This process is modelled as a random walk in a layered one-dimensional material, where each layer has a distinct particle hopping rate. Particles are released at some location, and the duration of time taken for each particle to reach an absorbing boundary is recorded. To explore whether these data can be used to identify the hopping rates in each layer, we compute various profile likelihoods using two methods: first, an exact likelihood is evaluated using a relatively expensive Markov chain approach; and, second, we form an approximate likelihood by assuming the distribution of exit times is given by a Gamma distribution whose first two moments match the moments from the continuum limit description of the stochastic model. Using the exact and approximate likelihoods, we construct various profile likelihoods for a range of problems. In cases where parameter values are not identifiable, we make progress by re-interpreting those data with a reduced model with a smaller number of layers.
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22

Slud, Eric V., and Filia Vonta. "Efficient semiparametric estimators via modified profile likelihood." Journal of Statistical Planning and Inference 129, no. 1-2 (February 2005): 339–67. http://dx.doi.org/10.1016/j.jspi.2004.06.057.

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23

Pace, Luigi, Alessandra Salvan, and Laura Ventura. "Adjustments of profile likelihood through predictive densities." Annals of the Institute of Statistical Mathematics 63, no. 5 (February 24, 2010): 923–37. http://dx.doi.org/10.1007/s10463-010-0274-9.

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24

Subramanian, Sundarraman. "Censored median regression and profile empirical likelihood." Statistical Methodology 4, no. 4 (October 2007): 493–503. http://dx.doi.org/10.1016/j.stamet.2007.05.002.

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25

Martins-Filho, Carlos, and Feng Yao. "Semiparametric Stochastic Frontier Estimation via Profile Likelihood." Econometric Reviews 34, no. 4 (November 7, 2014): 413–51. http://dx.doi.org/10.1080/07474938.2013.806729.

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26

Stafford, James E. "A robust adjustment of the profile likelihood." Annals of Statistics 24, no. 1 (February 1996): 336–52. http://dx.doi.org/10.1214/aos/1033066212.

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27

Li, Minqiang, Liang Peng, and Yongcheng Qi. "Reduce computation in profile empirical likelihood method." Canadian Journal of Statistics 39, no. 2 (May 23, 2011): 370–84. http://dx.doi.org/10.1002/cjs.10101.

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28

Hinkley, D. V. "Modified Profile Likelihood in Transformed Linear Models." Applied Statistics 38, no. 3 (1989): 495. http://dx.doi.org/10.2307/2347736.

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29

Royston, Patrick. "Profile Likelihood for Estimation and Confidence Intervals." Stata Journal: Promoting communications on statistics and Stata 7, no. 3 (September 2007): 376–87. http://dx.doi.org/10.1177/1536867x0700700305.

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Normal-based confidence intervals for a parameter of interest are inaccurate when the sampling distribution of the estimate is nonnormal. The technique known as profile likelihood can produce confidence intervals with better coverage. It may be used when the model includes only the variable of interest or several other variables in addition. Profile-likelihood confidence intervals are particularly useful in nonlinear models. The command pllf computes and plots the maximum likelihood estimate and profile likelihood–based confidence interval for one parameter in a wide variety of regression models.
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30

COX, D. R., and N. REID. "A note on the difference between profile and modified profile likelihood." Biometrika 79, no. 2 (1992): 408–11. http://dx.doi.org/10.1093/biomet/79.2.408.

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31

Capielo Rosario, Cristalis, Hector Y. Adames, Nayeli Y. Chavez-Dueñas, and Roberto Renteria. "Acculturation Profiles of Central Florida Puerto Ricans: Examining the Influence of Skin Color, Perceived Ethnic-Racial Discrimination, and Neighborhood Ethnic-Racial Composition." Journal of Cross-Cultural Psychology 50, no. 4 (March 21, 2019): 556–76. http://dx.doi.org/10.1177/0022022119835979.

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Evaluating sociocultural factors that may influence acculturation strategies rather than assuming homogeneity among different Latinx ethnic groups is important. A latent profile analysis with covariates was used to identify acculturation profiles in a sample of first-generation Central Florida Puerto Ricans ( N = 381) along bidimensional behavioral, values, and ethnic identity indicators. We examined whether three contextual covariates including (a) perceived ethnic-racial discrimination, (b) percentage of White Americans, and (c) percentage of Puerto Ricans residing in each participants’ zip code could help derive latent profile membership. Participants were categorized into three profiles. The first profile exhibited the highest levels of White American ethnic identity and high levels of Puerto Rican and White American cultural behaviors. The second profile described individuals with the lowest adherence to White American behaviors and ethnic identity. It also exhibited high attachment to Puerto Rican cultural values. The third profile exhibited high levels of Puerto Rican and White American cultural values and moderate levels of White American cultural behaviors and ethnic identity. An examination of covariates revealed that only perceived ethnic-racial discrimination had an influence on profile identification and membership, with likelihood of belonging to Profile 2 decreasing, and likelihood of belonging to Profile 1 increasing as perceived ethnic-racial discrimination increased. Perceived ethnic-racial discrimination did not influence the likelihood of Profile 3 membership. Results highlight the importance of contextualizing acculturation.
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32

BARNDORFF-NIELSEN, O. E. "Stable and invariant adjusted profile likelihood and directed likelihood for curved exponential models." Biometrika 82, no. 3 (1995): 489–99. http://dx.doi.org/10.1093/biomet/82.3.489.

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33

Hirose, Yuichi. "Efficiency of profile likelihood in semi-parametric models." Annals of the Institute of Statistical Mathematics 63, no. 6 (March 31, 2010): 1247–75. http://dx.doi.org/10.1007/s10463-010-0280-y.

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34

Tsimikas, John V., Ronald J. Bosch, Brent A. Coull, and Hammou El Barmi. "Profile-Likelihood Inference for Highly Accurate Diagnostic Tests." Biometrics 58, no. 4 (December 2002): 946–56. http://dx.doi.org/10.1111/j.0006-341x.2002.00946.x.

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35

Chen, Ziqi, Man-Lai Tang, and Wei Gao. "A profile likelihood approach for longitudinal data analysis." Biometrics 74, no. 1 (April 25, 2017): 220–28. http://dx.doi.org/10.1111/biom.12712.

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36

Tönsing, Christian, Jens Timmer, and Clemens Kreutz. "Profile likelihood-based analyses of infectious disease models." Statistical Methods in Medical Research 27, no. 7 (March 7, 2018): 1979–98. http://dx.doi.org/10.1177/0962280217746444.

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Ordinary differential equation models are frequently applied to describe the temporal evolution of epidemics. However, ordinary differential equation models are also utilized in other scientific fields. We summarize and transfer state-of-the art approaches from other fields like Systems Biology to infectious disease models. For this purpose, we use a simple SIR model with data from an influenza outbreak at an English boarding school in 1978 and a more complex model of a vector-borne disease with data from the Zika virus outbreak in Colombia in 2015–2016. Besides parameter estimation using a deterministic multistart optimization approach, a multitude of analyses based on the profile likelihood are presented comprising identifiability analysis and model reduction. The analyses were performed using the freely available modeling framework Data2Dynamics (data2dynamics.org) which has been awarded as best performing within the DREAM6 parameter estimation challenge and in the DREAM7 network reconstruction challenge.
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37

Severini, T. "An approximation to the modified profile likelihood function." Biometrika 85, no. 2 (June 1, 1998): 403–11. http://dx.doi.org/10.1093/biomet/85.2.403.

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38

Lin, Lu, Lixing Zhu, and K. C. Yuen. "Profile empirical likelihood for parametric and semiparametric models." Annals of the Institute of Statistical Mathematics 57, no. 3 (September 2005): 485–505. http://dx.doi.org/10.1007/bf02509236.

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39

Shalabh. "Meta-analysis of Binary Data using Profile Likelihood." Journal of the Royal Statistical Society: Series A (Statistics in Society) 173, no. 3 (January 4, 2010): 691. http://dx.doi.org/10.1111/j.1467-985x.2010.00646_2.x.

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40

Montoya, José A., Eloísa Díaz-Francés, and David A. Sprott. "On a criticism of the profile likelihood function." Statistical Papers 50, no. 1 (March 1, 2007): 195–202. http://dx.doi.org/10.1007/s00362-007-0056-5.

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41

Montiel Ishino, Francisco A., Claire Rowan, Rina Das, Janani Thapa, Ewan Cobran, Martin Whiteside, and Faustine Williams. "Identifying Risk Profiles of Malignant Prostate Cancer Surgical Delay Using a Person-Centered Approach to Understand Prostate Cancer Disparities: The Constellation of Health Determinants Using Latent Class Analysis on Cancer Registry Data." American Journal of Men's Health 14, no. 6 (November 2020): 155798832098428. http://dx.doi.org/10.1177/1557988320984282.

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Surgical prostate cancer (PCa) treatment delay (TD) may increase the likelihood of recurrence of disease, and influence quality of life as well as survival disparities between Black and White men. We used latent class analysis (LCA) to identify risk profiles in localized, malignant PCa surgical treatment delays while assessing co-occurring social determinants of health. Profiles were identified by age, marital status, race, county of residence (non-Appalachian or Appalachian), and health insurance type (none/self-pay, public, or private) reported in the Tennessee Department of Health cancer registry from 2005 to 2015 for adults ≥18 years ( N = 18,088). We identified three risk profiles. The highest surgical delay profile (11% of the sample) with a 30% likelihood of delaying surgery >90 days were young Black men, <55 years old, living in a non-Appalachian county, and single/never married, with a high probability of having private health insurance. The medium surgical delay profile (46% of the sample) with a 21% likelihood of delay were 55–69 years old, White, married, and having private health insurance. The lowest surgical delay profile (42% of the sample) with a 14% likelihood of delay were ≥70 years with public health insurance as well as had a high probability of being White and married. We identified that even with health insurance coverage, Blacks living in non-Appalachian counties had the highest surgical delay, which was almost double that of Whites in the lowest delay profile. These disparities in PCa surgical delay may explain differences in health outcomes in Blacks who are most at-risk.
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42

Ionides, E. L., C. Breto, J. Park, R. A. Smith, and A. A. King. "Monte Carlo profile confidence intervals for dynamic systems." Journal of The Royal Society Interface 14, no. 132 (July 2017): 20170126. http://dx.doi.org/10.1098/rsif.2017.0126.

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Monte Carlo methods to evaluate and maximize the likelihood function enable the construction of confidence intervals and hypothesis tests, facilitating scientific investigation using models for which the likelihood function is intractable. When Monte Carlo error can be made small, by sufficiently exhaustive computation, then the standard theory and practice of likelihood-based inference applies. As datasets become larger, and models more complex, situations arise where no reasonable amount of computation can render Monte Carlo error negligible. We develop profile likelihood methodology to provide frequentist inferences that take into account Monte Carlo uncertainty. We investigate the role of this methodology in facilitating inference for computationally challenging dynamic latent variable models. We present examples arising in the study of infectious disease transmission, demonstrating our methodology for inference on nonlinear dynamic models using genetic sequence data and panel time-series data. We also discuss applicability to nonlinear time-series and spatio-temporal data.
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43

Kolassa, John E. "Approximate multivariate conditional inference using the adjusted profile likelihood." Canadian Journal of Statistics 32, no. 1 (March 2004): 5–14. http://dx.doi.org/10.2307/3315995.

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44

Pace, Luigi, and Alessandra Salvan. "Adjustments of the profile likelihood from a new perspective." Journal of Statistical Planning and Inference 136, no. 10 (October 2006): 3554–64. http://dx.doi.org/10.1016/j.jspi.2004.11.016.

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45

Bartolucci, F., R. Bellio, A. Salvan, and N. Sartori. "Modified Profile Likelihood for Fixed-Effects Panel Data Models." Econometric Reviews 35, no. 7 (October 22, 2014): 1271–89. http://dx.doi.org/10.1080/07474938.2014.975642.

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46

Lam, Clifford, and Jianqing Fan. "Profile-kernel likelihood inference with diverging number of parameters." Annals of Statistics 36, no. 5 (October 2008): 2232–60. http://dx.doi.org/10.1214/07-aos544.

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47

Ferrari, Silvia L. P., Michel Ferreira Da Silva, and Francisco Cribari-Neto. "Adjusted Profile Likelihood for Two-Parameter Exponential Family Models." Communications in Statistics - Theory and Methods 34, no. 2 (January 2005): 257–76. http://dx.doi.org/10.1080/03610920509342419.

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48

Gimenez, Olivier, Rémi Choquet, Laurent Lamor, Paul Scofield, David Fletcher, Jean-Dominique Lebreton, and Roger Pradel. "Efficient profile-likelihood confidence intervals for capture-recapture models." Journal of Agricultural, Biological, and Environmental Statistics 10, no. 2 (June 2005): 184–96. http://dx.doi.org/10.1198/108571105x46462.

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49

Banerjee, Samprit, Stefano Monni, and Martin T. Wells. "A regularized profile likelihood approach to covariance matrix estimation." Journal of Statistical Planning and Inference 179 (December 2016): 36–59. http://dx.doi.org/10.1016/j.jspi.2016.06.004.

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50

Algeri, Sara, Jelle Aalbers, Knut Dundas Morå, and Jan Conrad. "Searching for new phenomena with profile likelihood ratio tests." Nature Reviews Physics 2, no. 5 (April 28, 2020): 245–52. http://dx.doi.org/10.1038/s42254-020-0169-5.

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